Part A
Construct a circle of any radius, and draw a chord on it. Then construct the radius of the circle that bisects the chord. Measure the angle between the chord and the radius. What can you conclude about the intersection of a chord and the radius that bisects it? Take a screenshot of your construction, save it, and insert the image below your answer.
Part B
Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii OA and OC.
Part C
In this part of the activity, you will investigate the converse of the theorem stated in part A. To get started, reopen GeoGebra.
Draw a circle of any radius, and draw a chord on it. Construct the radius of the circle that is perpendicular to the chord. Measure the line segments into which the radius divides the chords. How are the line segments related? What can you conclude about the intersection of a chord and a radius that is perpendicular to it? Take a screenshot of your construction, save it, and insert the image below your answer.
Part D
Write a paragraph proof of your conclusion in part C. To begin your proof, draw radii OA and OC.
Answers
Answer:
All answers are bold and links are real photos
BTW THE PHOTOS ARE IN ORDER OF THE ANSWERS
Brainlyist??
Step-by-step explanation:
Task 1
Part A
Tangent Line
Part B
PHOTO WITH LARGE CIRCLE AND LINE OUT SIDE BUT CONNECTED
Part C
2034.7
PHOTO WITH EQUATION
We calculate the point from the center of the earth to the satellite and because we have the radius we can subtract it getting the distance from the satellite to the earth.
Task 2
Gears
Part A
Approximately 10.47 inches
Part B
300°
Part C
Approximately 125.66 inches
Part D
The distance traveled increases by approximately 62.83 inches
Task 3
Circle Theorems
Part A
PHOTO WITH LINE THROUGH CIRCLE AND ONE 90 DEGREE ANGLE
Part B
Prove OC is perpendicular to AB
We know that ΔAEC≅AED by SSS criteria (SSS criteria is when all three sides of a triangle is equal making them congruent)
To prove this that they apply to the SSS criteria: m∠ADO=m∠BDO m∠ADO=90°=m∠BDO
Part C
A radius is perpendicular to a chord when the chord is equally divided in half by the radius.
PHOTO OF LINE THROUGH CIRCLE AND LINE DISTANCES
Part D
Prove OC is perpendicular to AB
AO=BO because AO and BO are both radii
OD≅OD by reflexive theorem
ΔADO≅ΔBDO because they are both right triangle with the hypotenuse and a side
AB≅BC means that OC is perpendicular to AB
Disclaimer: The images to part A and part C is the same.
Two theorems we are proving are:
Line drawn from the center of the circle to bisect a chord is perpendicular to it.Perpendicular drawn from the center of the circle to a chord, bisects it.How do we solve the given question?Part A: The image is attached
Part B:
Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE bisects AC at B, that is, AB = BC.
To prove: A line drawn from the center of the circle to bisect a chord is perpendicular to it.
Construction: We join OA and OB.
Proof:
In ΔOAB and ΔOCB,
OA = OC (Radius of the same circle)
AB = BC (Given, at B, the chord is bisected)
OB = OB (common side)
∴ ΔOAB ≅ ΔOCB [SSS axiom]
∴ ∠OBA = ∠OBC [Common parts of Congruent triangles]
Let ∠OBA = ∠OBC = x.
Since AC is a straight line,
∠OBA + ∠OBC = 180° [Linear pair]
or, x + x = 180°
or, 2x = 180°
or, x = 90°.
∴ ∠OBA = ∠OBC = 90°.
So, we can say that OB ⊥ AC, hence the theorem is proved.
Part C: The image is attached
Part D:
Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE is perpendicular to AC at B, that is, AB ⊥ BC.
To prove: A line drawn from the center of the circle perpendicular to the chord bisects it.
Construction: We join OA and OB.
Proof:
In ΔOAB and ΔOCB,
OA = OC (Radius of the same circle)
∠OBA = ∠OBC = 90° (∵ OB ⊥ AC)
OB = OB (common side)
∴ ΔOAB ≅ ΔOCB [RHS axiom]
∴ AB = AC [Common parts of Congruent triangles]
So, we can say that OE perpendicular to the chord AC bisects it, hence the theorem is proved.
Learn more about chord properties at
https://brainly.com/question/13950364
#SPJ2
Related Questions
what is the easiest way to find length in volume
Answers
Answer:
Step-by-step explanationthe easiest way to find the length in volume is by first knowing it's formular wich is L x Wx H= length x width x height
Plis help me with the blank spaces !!!! They give me those 4 options as well in the second one
Answers
The total points earned depends on the number of correct answers.
Hope this helps!
Makati and his friends rolled two fair number cubes 500 times and recorded the sum of the numbers shown on the cubes each time. On 42 of the trails sum was 10. Which of these is fair number cubes are rolled
Answers
Answer:
1/2 anwser is B
Step-by-step explanation:
rolled 2 fair number 500 times right? okay so the sum is a number of anytotal added up correct?
it was shown on the cubes each time ,so you can assume wit 42+10=52?2=x well then just divide that by 500! wich is 1/2
Can I have help on this?
Answers
The price of an item yesterday was 105. Today, the price rose to 147 find the percentage increase
Answers
Answer:
40%
Step-by-step explanation:
147 - 105 = 42
42/105 = .4
.4 × 100 = 40%
If f(x) = 3x + 5 and g(x) = -2x - 5x+3, find (f + g)(x).
O A. (f+ g)(x) = -2x + 8
O B. (f + g)(x) = -4x + 8
OC. (f+ g)(x) = -2x2 + 8x+ 8
OD. (f + g)(x) = -2x2 - 2x + 8
Answers
Answer:
D. (f + g)(x) = -2x² - 2x + 8
Step-by-step explanation:
Given:
f(x) = 3x + 5g(x) = -2x² - 5x + 3Find (f + g)(x):
⇒ [tex]f(x) + f(g)[/tex]
⇒ [tex]3x + 5 + ( -2x^{2} - 5x + 3 )[/tex]
⇒ [tex]3x + 5 - 2x^{2} - 5x + 3[/tex]
Combine like terms:
⇒ [tex]-2x^{2} + 3x - 5x + 5 + 3[/tex]
⇒ [tex]-2x^{2} - 2x + 8[/tex]
Answer: D. (f + g)(x) = -2x² - 2x + 8
may you please answer this question
Answers
Answer:
Step-by-step explanation:
Vertically opposite angles are congruent.
∠A = ∠C
∠A + ∠C = 254
∠A + ∠A = 254
2∠A = 254
∠A = 254/2
∠A = 127
Linear Pair: In two adjacent angles, if the non common arms are opposite rays, then they are called linear and they add up to 180
∠A + ∠B = 180 {linear pair}
127 + ∠B = 180
∠B = 180- 127
∠B = 53°
What is Arrhenius's definition of an acid?
O a substance that dissociates in water to produce hydroxide ions (OH)
O a substance that dissociates.in water to produce hydrogen ions (H+).
o
any substance that can donate hydrogen ions (H+)
Answers
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
Arrhenius theory of an acid: This theory was discovered by Sir Svante Arrhenius in 1887. According to this theory acids are hydrogen containing compounds, when dissolves in water it gives (H+) ions.
[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Question:}}}}}}[/tex]
[tex] \sf \red{What \: is \: Arrhenius's \: definition \: of \: an \: acid?}[/tex]
[tex] \implies[/tex] (B) substance that dissociates.in water to produce hydrogen ions (H+).So, option (B) is correct.
[tex] \boxed{ \frak \red{happy \: learning}}[/tex]
If ∠G measures 40°, ∠F measures 49°, and f is 7 feet, then find g using the Law of Sines. Round your answer to the nearest foot.
4 feet
5 feet
6 feet
7 feet
Answers
Answer:
6 feet
Step-by-step explanation:
took the test and got it right
Answer:
6 feet
Step-by-step explanation:
(c) 6 feet
11. If mNJ = "
170", mMK = (5x + 8), and mZMLK = (4x + 3)", find mZMLK.
,
M
o
K
Answers
Answer:
∠ MLK = 51°
Step-by-step explanation:
the secant- secant angle MLK is half the difference of the measures of the intercepted arcs , that is
∠ MLK = [tex]\frac{1}{2}[/tex] ( NJ - MK ) ← substitute values
4x + 3 = [tex]\frac{1}{2}[/tex] (170 - (5x + 8) ) ← multiply both sides by 2 to clear the fraction
8x + 6 = 170 - 5x - 8
8x + 6 = 162 - 5x ( add 5x to both sides )
13x + 6 = 162 ( subtract 6 from both sides )
13x = 156 ( divide both sides by 13 )
x = 12
Then
∠ MLK = 4x + 3 = 4(12) + 3 = 48 + 3 = 51°
What is the equation of a line that crosses the x-axis at 36 and is perpendicular to the line y=-4/9+5
Answers
Answer:
Step-by-step explanation:
Given, line equation is
We have to find the line equation which is perpendicular to the given line in slope intercept form.
Now, let us find the slope of the given line.ven line is in slope intercept form,
y = mx + c where m is slope and c is intercept.
So, by comparison, slope of given line is
Now, we know that product of slopes of perpendicular lines = -1
SLope of that perpendicular line And we are also given that, perpendicular line passes x aixs at 36. Which means that intercept of x – axis is 36.
3.4k+(0.63−0.81k)÷0.9=5.7
Answers
Part I: Converting the terms into fraction form
Given equation:
3.4k + (0.63 - 0.81k) ÷ 0.9 = 5.7First, let's convert the terms (that are in decimals) into fractions.
3.4k = 34k/100.63 = 63/1000.81k = 81k/1000.9 = 9/105.7 = 57/10Replace the fraction forms in the equation:
3.4k + (0.63 - 0.81k) ÷ 0.9 = 5.734k/10 + (63/100 - 81k/100) ÷ 9/10 = 57/10Part II: Simplifying the division being performed
Since the expression in the parenthesis can't be simplified, we can open the parenthesis. Before we do that, we need to divide the expression by 9/10 (as division is third in BODMAS). This can be done by converting the divisor into it's reciprocal and changing the sign to a multiplication sign.
34k/10 + (63/100 - 81k/100) × 10/9 = 57/10Since there is no other division being performed, we can simplify the distributive property (as multiplication is fourth in BODMAS).
34k/10 + [63/100 × 10/9] - [81k/100 × 10/9] = 57/1034k/10 + [7/10] - [9k/10] = 57/1034k/10 + 7/10 - 9k/10 = 57/10Part III: Isolating "k" to determine it's value
Combine like terms as needed:
34k/10 + 7/10 - 9k/10 = 57/10k(34/10 - 9/10) + 7/10 = 57/1025k/10 + 7/10 = 57/10Subtract 7/10 both sides of the equation to isolate "x" and it's coefficient.
25k/10 + 7/10 - 7/10 = 57/10 - 7/1025k/10 = 50/10Cancel the denominators (as a/b = c/b ⇔ a = c)
25k/10 = 50/1025k = 50Divide both sides by 25 to isolate "k"
25k/25 = 50/25k = 2GIVING BRAINLEST TO THE PERSON THAT CAN EXPLAIN HOW TO DO THIS THE BEST :)
Answers
Answer:
I think area will me 24 sq unit
Explanation:
AC=6
BD=8
1/2 × 8 × 6 = 24
The answer is 24units or the second selection.
According to this box plot of test scores, the top 25% of the students scored about what score?
options:
86
100
96
90
Answers
96
In this type of box plot, the two end lines are the absolute maximum and minimum values, each edge of the box is the lower and upper 25%, respectively from left to right, and the line in the box is 50%
So the answer here is the right edge of the box, or 96
How many degrees is the angle measurement of x?
Answers
Answer:
x ≈ 37.13°
Step-by-step explanation:
using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{13.4}{22.2}[/tex] , then
x = [tex]sin^{-1}[/tex] ( [tex]\frac{13.4}{22.2}[/tex] ) ≈ 37.13° ( to the nearest hundredth )
The base area of a cylinder is 200.96m2
and the volume is 1205.76 in3
. what is the height of the cylinder?
Answers
Answer:
Step-by-step explanation:
Volume of cylinder = base area * height
height of the cylinder = Volume of the cylinder ÷ base area
= 1205.76 ÷ 200.96
= 6 in
Sophie and Marcos are each saving for new bicycles. So far, Sophie has $7 saved and can earn $4 per hour walking dogs. Marcos has $3 saved and can earn $6 per hour at his family's plant nursery. After how many hours of work will Sophie and Marcos have saved the same amount? What will that amount be? Use the system of equations below to complete the graph.
Answers
Answer:
2 hours
Step-by-step explanation:
You can express each person's total earning as the formula for a line. (y=mx+b) Use the amount per hour that can be earned as the slope (m) and the amount already earned as the y intercept (b)
Sophie: y=4x+7
Marcos: y=6x+3
Since y is the total amount of money saved and you know that both people need to earn the same amount of money, we know that y is the same in both equations so we can use substitution to substitute one of the equations in for y in the other equation like this:
4x+7=6x+3
From here, solve algebraically
Subtract 3
4x+4=6x
Subtract 5x
4=2x
Divide by 2
x=2
So they will have the same amount of money after 2 hours.
A company is considering adding a new ingredient to its bread recipe to increase the freshness of the bread. to study the impact of adding ingredient p, q, r, s, or t to the recipe, they baked 270 loaves of bread. some of the loaves contained no extra ingredients, while each of the rest contained one of the five new ingredients. the freshness of the bread was checked one week later, and the results were used to create the two-way tables below. which tables suggest an association between adding an extra ingredient and the freshness of the bread? select the three correct answers. a 3-column table with 2 rows titled effect of ingredient p on freshness. column 1 has entries contains the ingredient, does not contain the ingredient. column 2 is labeled stays fresh with entries 11, 4. column 3 is labeled does not stay fresh with entries 39, 16. a 3-column table with 2 rows titled effect of ingredient q on freshness. column 1 has entries contains the ingredient, does not contain the ingredient. column 2 is labeled stays fresh with entries 9, 4. column 3 is labeled does not stay fresh with entries 41, 16. a 3-column table with 2 rows titled effect of ingredient r on freshness. column 1 has entries contains the ingredient, does not contain the ingredient. column 2 is labeled stays fresh with entries 16, 4. column 3 is labeled does not stay fresh with entries 34, 16. a 3-column table with 2 rows titled effect of ingredient s on freshness. column 1 has entries contains the ingredient, does not contain the ingredient. column 2 is labeled stays fresh with entries 4, 4. column 3 is labeled does not stay fresh with entries 46, 16. a 3-column table with 2 rows titled effect of ingredient t on freshness. column 1 has entries contains the ingredient, does not contain the ingredient. column 2 is labeled stays fresh with entries 34, 4. column 3 is labeled does not stay fresh with entries 16, 16.
Answers
Answer:
Tables 3,4 and 5
Step-by-step explanation:
Answer on quizlet.
Answer:
h
Step-by-step explanation:
Please solve the attached problem with all steps.
Answers
Answer:
x = 8
Step-by-step explanation:
Theorem
When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Secant: a straight line that intersects a circle at two points
Tangent: a straight line that touches a circle at only one point
Given:
tangent segment = xsecant segment = 4 + 12 = 16external secant segment = 4⇒ x² = 16 · 4
⇒ x² = 64
⇒ x² = √(64)
⇒ x = ±8
As distance is positive, x = 8
The radius of a circular swimming pool is 7.8 meters. Which is closest to the circumference of this swimming pool?
f 48.98 m g 191.04 m h 24.49 m j 47.76 m
Answers
Answer:
F. 48.98 m
Step-by-step explanation:
What is circumference?
The circumference of a circle is the distance around the circle, otherwise known as the perimeter.The formula to find the circumference of a circle is 2πr, or if you're given the diameter, πdHow does it apply here?
We are asked to find the closest circumference given of the swimming pool. We are also given the radius of the pool as 7.8 meters.Solving
Step 1: Plug in your values.
[tex]2 * 3.14 * 7.8[/tex]Step 2: Simplify.
[tex](2*3.14)*7.8 = 6.28 * 7.8[/tex] [tex]6.28 *7.8 = 48.984[/tex] 48.984 ≈ 48.98Therefore, the correct answer is F. 48.98 meters.
(24 +2)divide by 2 order operation
Answers
Answer:
13
Step-by-step explanation:
(24+2)/2 would be the expression.
PEMDAS so first complete the numbers in the Parantheseis:
(24+2)/2 = 26/2
Since there are no exponents or mulitplication, divide:
26/2 = 13
Hope this helps!
Which number sentence is true?
A. 30.678 > 31.112
B. 81.001 > 80.999
C. 24.510 = 24.5
D. 72.49 < 72.469
Answers
Answer:
B
Step-by-step explanation:
31.112 is actually greater than 30.678 because 31 is a greater number than 30. so the statement stated is false.
24.510 is greater than 24.5 because if you add 2 zeros to 24.5, it would be 24.500(adding zeros after decimal point doesnt change the value). 24.500 is less than 24.510. the numbers are not equal.
72.49 is greater than 72.469 because if you add a zero to 72.49, it will be 72.490. 72.490 is greater than 72.469.
Basically only B is true because 81 is greater than 80.
Don’t mind my answers I got them wrong but can you please help? I’ll award brainliest
Answers
Answer:
y=mx+b
Step-by-step explanation:
use that formula
A relay race covers a distance of 2 1/2 miles. Each runner on the team will run 1/4 mile. How many runners are needed for the team to cover the total distance of the race?
Answers
Answer:
6
Step-by-step explanation:
10 runners
explanation:
1/4 x 10 = 2 1/2
What rule can be used to find the next term of the sequence? an = an–1 – 79 an = an–1 – 13 an = an–1 13 an = an–1 79
Answers
The rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]
Its nth term is
[tex]T_n = a + (n-1)d[/tex]
(for all positive integer values of n)
And thus, the common difference is
[tex]T_{n+1} - T_n[/tex]
for all positive integer values of n
Here, the considered sequence is 27, 40, 53, 66, 79,...
We see that:
40-27=13
53-40=13
and so on, the difference between each consequtive pair of terms of this sequence is 13.
Thus, due to having common difference in consequtive terms, this is an arithmetic sequence.
For this series, we've got:
Initial term = a = 27Common difference = d = 13Thus, its nth term is given by:
[tex]T_n = a+(n-1)d= 27 +(n-1)13 = 13n + 14[/tex]
Since the options are using the notation [tex]a_n[/tex] instead of [tex]T_n[/tex], so we will use that too. Thus, nth term and (n-1)th terms are:
[tex]a_n = 13n + 14\\a_{n-1} = 13(n-1) + 14 = 13n + 1\\[/tex]
Thus, we can write nth term in the form of (n-1)th term as:
[tex]a_n = 13n + 14 = 13n + 1 + 13 = a_{n-1} + 13\\\\a_n = a_{n-1} + 13[/tex]
Thus, the rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
Answer:
c
Step-by-step explanation:
if x and y are real numbers greater than 1, what is the value of the expression log_x 1 + log_y y?
Answers:
A) 1
B) 0
C) 2
Answers
[tex]\log_x (1)+\log_y (y)\\\\=\log_x x^0 + 1\\\\=0\cdot \log_x x +1\\\\=0+1\\\\=1[/tex]
The ratio of red to blue marbles in the bag is 5 to 3. If there are 20 less blue marbles than red, how many blue marbles are in the bag?
Answers
Answer:
30
Step-by-step explanation:
red : blue = 5:3
since difference between 5&3 is automatically 2....then just add 0 to 3
A store pays $50 for a pair of shoes. The markup is 25%
Answers
Answer:
Are you asking for the selling price? If yes the answer should be $50 x (1+25%) = $62.5
75 ounces 5 pounds which one is greater
Answers
Answer:
5 pounds
Step-by-step explanation:
5 pounds is 80 ounces, which is greater then 75 ounces.
Multiply and simplify. 11 18 × − 4 11
A) − 7 27
B) − 2 9
C) 5 9
D) 11 27
Answers
Answer:
B) − 2/9
Explanation:
[tex]\hookrightarrow \sf \dfrac{11}{18} * -\dfrac{4}{11}[/tex]
join both fractions
[tex]\hookrightarrow \sf \dfrac{11*-4}{18*11}[/tex]
simplify by multiplying
[tex]\hookrightarrow \sf \dfrac{-44}{198}[/tex]
simplify the following
[tex]\hookrightarrow \sf -\dfrac{2}{9}[/tex]
[tex]\bold{Heya!}[/tex]
→ Answer :-B) [tex]\sf{-\frac{2}{9}[/tex]→ EXPLANATION :[tex]\sf{\frac{11}{18}(-\frac{4}{11})[/tex]
Apply rule : [tex]\sf{a(-b) = -ab}[/tex]
[tex]\sf{\frac{11}{18}(-\frac{4}{11}) = -\frac{11}{18}[/tex] × [tex]\sf{\frac{4}{11}[/tex]
[tex]\sf{= -\frac{11}{18}[/tex] × [tex]\sf{\frac{4}{11}[/tex]
Cross - cancel common factor: [tex]\sf{11}[/tex]
[tex]\sf{= -\frac{4}{18}[/tex]
Factor the number: [tex]\sf{4 = 2}[/tex] × [tex]\sf{2}[/tex]
[tex]\sf{= -\frac{2 \: x \: 2}{18}[/tex]
Factor the number: [tex]\sf{ 18 = 2 \: x \: 9}[/tex]
[tex]\sf{= - \frac{2 \: x \: 2}{2 \: x \: 9}[/tex]
Cancel common factor: [tex]\sf{2}[/tex]
[tex]\sf{-\frac{2}{9}[/tex]
Hopefully This Helps ! ~
#LearnWithBrainly
[tex]\underline{Answer :}[/tex]
Jaceysan ~