MathDB

Two non-intersecting circles,

\omega

and

\Omega

, have centers

C_\omega

and

C_\Omega

respectively. It is given that the radius of

\Omega

is strictly larger than the radius of

\omega

. The two common external tangents of

\Omega

and

\omega

intersect at a point

P

, and an internal tangent of the two circles intersects the common external tangents at

X

and

Y

. Suppose that the radius of

\omega

4

, the circumradius of

\triangle PXY

9

, and

XY

bisects

\overline{PC_\Omega}

. Compute

XY

Problem Statement