MathDB

A pentagon is inscribed in a circle, such that the pentagon has an incircle. All

10

sets of

3

vertices from the pentagon are chosen, and the incenters of each of the

10

resulting triangles are drawn in. Prove these

10

incenters lie on

2

concentric circles.
Note: I spent nearly no time on this, so if anyone took CMO and I misremembered just let me know.

Problem Statement