What is the length of chord XY

Question

asked May 19, 2020 204k views

1 Answer

Saustrup · Answer 1 · 2020-05-24T16:12:57+0000

Answer:

|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
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