Question

What is the length of chord XY

Answer 1

`|XY|=18cm`

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=√(81)=9`

The length of the chord is

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

The correct answer is A