Question

OA and OB are congruent. CD is a chord of both circles.If a radius is 20 ft and CD = 32 ft, how long is AB?

Answer 1

EXPLANATION

We can apply the Pythagorean Theorem as shown as follows:

`c^2=a^2+b^2`

If the radius is 20 ft, then c=20 ft

If CD = 32 ft, then b= CD/2 = 32/2 = 16 ft

Replacing terms:

`20^2=a^2+16^2`

Isolating a:

`20^2-16^2=a^2`

Computing the powers:

`400-256=a^2`

Applying the square root to both sides:

`\sqrt[]{400-256}=a`

Simplifying:

`\sqrt[]{144}=12=a`

The measure of AB is 12*2= 24 ft long