Circle A and circle B are congruent. CD is the

shadsiei

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 CD=24 in. What is the length of AB?

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

Answer & Explanation

grbavit

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,
CE=DE=12 inches
Now, in triangle ACE, BCE
AC=CB {radius of both circles are equal} ,side CE is common to both and angle AEC= CEB { both are of 90 degrees}
Therefore, triangle ACE is congruent to triangle BCE
Therefore, AE=EB
Step 2
Now, by Pythagorus theorem
AE=(AC)2(CE)2
AE=(13)2(12)2
AE=169144=5
AB=2AE=10 inches
Step 3
Ans: 10 inches

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