94.9k views
0 votes
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?

OA and OB are congruent. CD is a chord of both circles.If a radius is 20 ft and CD-example-1

1 Answer

1 vote

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

User Jisaacstone
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories