Resolved: "Circle A and circle B are congruent. CD..."

shadsiei

Answered question

2021-08-10

Circle A and circle B are congruent. CD is the chord of both circles. The radius is 13 in and

C D = 24

in. What is the length of AB?

a) 13 in
b) 20 in
c) 18 in
d) 10 in

grbavit

Skilled2021-08-11Added 109 answers

Step 1

Let Line CD meet AB at point E.
We know that perpendicular from center to chord bisect the chord, therefore,

C E = D E = 12

inches
Now, in triangle ACE, BCE

A C = C B

{radius of both circles are equal} ,side CE is common to both and angle

A E C = ∠ C E B

{ both are of 90 degrees}
Therefore, triangle ACE is congruent to triangle BCE
Therefore,

A E = E B

Step 2
Now, by Pythagorus theorem

A E = \sqrt{{(A C)}^{2} - {(C E)}^{2}}

A E = \sqrt{{(13)}^{2} - {(12)}^{2}}

A E = \sqrt{169 - 144} = 5

A B = 2 A E = 10

inches
Step 3
Ans: 10 inches

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?