Answer:
[tex]|XY|=18cm[/tex]
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 [tex]d[/tex] be the length of half of the chord. See diagram in attachment.
Then from Pythagoras Theorem,
[tex]d^2+12^2=15^2[/tex]
[tex]\Rightarrow d^2+144=225[/tex]
[tex]\Rightarrow d^2=225-144[/tex]
[tex]\Rightarrow d^2=81[/tex]
We take the positive square root of both sides to obtain,
[tex]d=\sqrt{81}=9[/tex]
The length of the chord is
[tex]2d=2(9)=18cm[/tex]
The correct answer is A
