Question

What is the length of chord XY

Answer 1

Answer:

$|XY|=18cm$

Step-by-step explanation:

Since the chord is a tangent to the smaller circle, it will meet the radius of the smaller circle at right angle.

Let $d$ be the length of half of the chord. See diagram in attachment.

Then from Pythagoras Theorem,

$d^2+12^2=15^2$

$\Rightarrow d^2+144=225$

$\Rightarrow d^2=225-144$

$\Rightarrow d^2=81$

We take the positive square root of both sides to obtain,

$d=\sqrt{81}=9$

The length of the chord is

$2d=2(9)=18cm$

The correct answer is A