MathDB

Let

\Gamma_1, \Gamma_2, \Gamma_3

be three pairwise externally tangent circles with radii

1,2,3,

respectively. A circle passes through the centers of

\Gamma_2

and

\Gamma_3

and is externally tangent to

\Gamma_1

at a point

P.

Suppose

A

and

B

are the centers of

\Gamma_2

and

\Gamma_3,

respectively. What is the value of

\frac{{PA}^2}{{PB}^2}?

Proposed by Kyle Lee

Problem Statement