Mathematics: What is the length of the radius of circle B?

What is the length of the radius of circle B?, №9534623, 24.09.2020 08:08

Mathematics

In circle O, chord AOB is drawn. Point C is located on the exterior of the circle with tangent CB and secant CDA drawn.Itisknownthat CD2 and DA6. (a) Determine the length of BC . (b) What is the length of the radius of circle O in simplest radical form. (c) Determine the measure of C . Hint - consider right triangle trigonometry instead of circle theorems. REASONING (d) Find the measure of AD . Show how you arrived at your answer.

Step-by-step answer

P Answered by PhD

21

(a) 4

(b) 2√3

(c) 60°

(d) 120°

Step-by-step explanation:

(a) The relationship between tangents and secants is ...

CB^2 = CD·CA

Filling in the given values, we find ...

CB^2 = 2·(2+6) = 16

CB = √16 = 4

The length of BC is 4 units.

__

(b) Triangle ABC is a right triangle, so the sides of it satisfy the Pythagorean theorem.

CA^2 = CB^2 +AB^2

8^2 = 16 +AB^2

AB = √48 = 4√3

The radius is half the length of AB, so the radius is 2√3.

__

(c) The measure of angle C can be determined from the cosine relation:

cos(C) = CB/CA = 4/8 = 1/2

C = arccos(1/2) = 60°

The measure of angle C is 60°.

__

(d) Arc AD is intercepted by angle ABD, which has the same measure as angle C. Hence the measure of arc AD is twice the measure of angle C.

The measure of arc AD is 120°.

Mathematics

In circle k , diameter cd is drawn and point e is located on the circle such that ce=16 and de=30 .what is the length of the radius of circle k?

Step-by-step answer

P Answered by PhD

11

The length of the radius of the circle K is $17\ units$

Step-by-step explanation:

we know that

The triangle CDE is a right triangle with the 90 degree angle at point E

so

Applying the Pythagoras Theorem

Find the length of CD (diameter of the circle K)

$CD^{2}=CE^{2}+DE^{2}$

substitute the values

$CD^{2}=16^{2}+30^{2}$

$CD^{2}=1,156$

$CD=34\ units$

Find the radius

Remember that the radius is half the diameter

so

$r=34/2=17\ units$

Mathematics

10 POINTS!! Made myself broke with my last two questions! The center of circle O is the origin. Circle O passes through the point (−5, −12). What is the length of the radius of circle O? A. √ 17 B. 7 C. √ 119 D. 13

Step-by-step answer

P Answered by PhD

1

D

Step-by-step explanation:

The radius r is the distance from the centre to a point on the circle.

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 5, - 12)

r = $\sqrt{(-5-0)^2+(-12-0)^2}$

= $\sqrt{(-5)^2+(-12)^2}$

= $\sqrt{25+144}$

= $\sqrt{169}$

= 13 → D

Mathematics

In circle M, segment AB is tangent to the circle at point C. AB has endpoints such that AM BM  , AC  9 and BC  4 . What is the length of the radius of circle M. Show how you arrived at your answer.

Step-by-step answer

P Answered by PhD

6

Step-by-step explanation:

We can use the geometric mean theorem:

The altitude on the hypotenuse is the geometric mean of the two segments it creates.

In your triangle, the altitude is the radius CM and the segments are AC and BC.

$CM = \sqrt{AC \times BC} = \sqrt{ 9 \times 4} = \sqrt{36} = \mathbf{6}\\\text{The radius of the circle M is $\large \boxed{\mathbf{6}}$}$

In circle M, segment AB is tangent to the circle at point C. AB has endpoints such that AM BM  , AC

Mathematics

In circle O, diameter AOB is drawn and point C is located on the circle such that CA=12 and CB=16. What is the length of the radius of circle O?

Step-by-step answer

P Answered by PhD

radius = 10

Step-by-step explanation:

As AB is the diameter of the circle, the angle ACB inscribes an arc of 180 degrees, so it is a 90 degrees angle, then the triangle ACB is a right triangle, with hypotenusa AB.

We can find the length of the diameter AB using the Pythagoras' theorem:

AB^2 = CA^2 + CB^2

AB^2 = 12^2 + 16^2 = 400

AB = 20

The radius of the circle is half the diameter, so the radius is 20 / 2 = 10

Mathematics

1) which circles are congruent? b and c b and d a and d 2)what is the length of the radius in circle c? 3 4 5 3)what is the name of the circle that has radius cl? a b c 4) which of the following is a radius of circle b? bn md nh 5)the diameter of circle a is ef ag eg fg 6)all of the following are radii except ag bh ij 7)what is the length of diameter ef ? 3 6 9 8)which circles have the same length radii? a and d b and c a and c

Step-by-step answer

P Answered by Specialist

40

Hello!

1) A and D

The radius is the distance from the center of a circle to any part of the edge. Both A and D have a radius of three, regardless of what direction they go.

2) 5"

In circle C we see that there is a line segment that is 5" that goes from the center to the edge, or the radius.

3) C

The different variables are representing different points on the circles. The circle that contains a line connecting C and L is circle C.

4) BN

Circle B contains a radius that is the distance from B to N, or BN.

5) EF

The diameter is the distance of a straight line that was pass through the middle of a circle, or its width. The diameter is double the radius. In circle A we see that line EF passes through the center put goes all the way across the circle.

6)IJ

Line IJ isn't even linear, so it could not be the radius. Both AG and BH are straight lines that represent the radius.

7) 6"

The diameter is always twice the radius. In circle A the radius is 3, so the diameter is 6.

8) A and D

Just as we said in the first answer, A and D both have a radius that measures 3 inches.

I hope this helps!

Mathematics

1) which circles are congruent? b and c b and d a and d 2)what is the length of the radius in circle c? 3 4 5 3)what is the name of the circle that has radius cl? a b c 4) which of the following is a radius of circle b? bn md nh 5)the diameter of circle a is ef ag eg fg 6)all of the following are radii except ag bh ij 7)what is the length of diameter ef ? 3 6 9 8)which circles have the same length radii? a and d b and c a and c

Step-by-step answer

P Answered by Specialist

40

Hello!

1) A and D

The radius is the distance from the center of a circle to any part of the edge. Both A and D have a radius of three, regardless of what direction they go.

2) 5"

In circle C we see that there is a line segment that is 5" that goes from the center to the edge, or the radius.

3) C

The different variables are representing different points on the circles. The circle that contains a line connecting C and L is circle C.

4) BN

Circle B contains a radius that is the distance from B to N, or BN.

5) EF

The diameter is the distance of a straight line that was pass through the middle of a circle, or its width. The diameter is double the radius. In circle A we see that line EF passes through the center put goes all the way across the circle.

6)IJ

Line IJ isn't even linear, so it could not be the radius. Both AG and BH are straight lines that represent the radius.

7) 6"

The diameter is always twice the radius. In circle A the radius is 3, so the diameter is 6.

8) A and D

Just as we said in the first answer, A and D both have a radius that measures 3 inches.

I hope this helps!

Mathematics

Suppose x is any positive number. Circle 1 has a center at (1, - 6) and a radius of 5x. Circle 2 has a center at (5, -1) and radius of 3x. Why is Circle 1 similar to Circle 2? Circle 1 and Circle 2 have the same circumference, and the radius of Circle 1 is 3/5 times the length of the radius of circle 2 Circle 1 is a translation of 4 units left and 5 units down from circle 2, and a dilation of circle 2 with a scale factor of 3/5. Circle 1 is a translation of 4 units left and 5 units down from circle 2, and a dilation of circle 2 with a scale factor

Step-by-step answer

P Answered by Specialist

I have no idea

Step-by-step explanation:

but here's this