MathDB

Three given circles have the same radius and pass through a common point

P

. Their other points of pairwise intersections are

A

B

C

. We define triangle

A'B'C'

, each of whose sides is tangent to two of the three circles. The three circles are contained in

\triangle A'B'C'

. Prove that the area of

\triangle A'B'C'

is at least nine times the area of

\triangle ABC

Problem Statement