Circle A and circle B intersect at points C and D. Each circle has radius 6 in. and AB = 8 in.

Question

What is CD?

Answer 1

Assuming that the value of AB = 8 in is the distance between the centers of each circle A and B, respectively.

 

• Set up a right triangle ACI where I is the intersection of the of CD and AB.
• AI is half of AB which is 1/2(8) = 4 in.
• AC is the radius of the circle r = 6 in.
• Use Pythagorean Theorem to find CI.

                   (AC)² = (CI)² + (AI)²

• 6² = CI² + 4²
• 36 = CI² + 16
• 36 - 16 = CI²
• 20 = CI²
• ±√20 = CI Use the positive value since distance cannot be negative.
• √20 = CI   Double this value to find CD.
• CI = 2* √20 = 2√20 in = 4√5 in.