Question

OA and OB are congruent. CD is a chord of both circles.If a radius is 15 ft and CD = 24 ft, how long is AB?

Answer 1

First, we have to identify the right triangle formed

As you can observe, segment AB is divided into two equal parts. We can find one part of AB using the Pythagorean's Theorem

$c^2=a^2+b^2$

Where c = 15 and b = 12. Let's find a

$\begin{gathered} 15^2=a^2+12^2 \\ 225=a^2+144 \\ 225-144=a^2 \\ a=\sqrt[]{81} \\ a=9 \end{gathered}$

Then, we know that AB = 2a, so

$AB=2\cdot a=2\cdot9=18ft$

Hence, AB is 18 feet long.