MathDB

3

Part of 2021 Peru MO (ONEM)

Problems(1)

3 incircles with radius r

Source: Peru National Olympiad 2021 #3

11/17/2021
Let M,N,PM,N,P be points in the sides BC,AC,ABBC,AC,AB of △ABC\triangle ABC respectively. The quadrilateral MCNPMCNP has an incircle of radius rr, if the incircles of △BPM\triangle BPM and △ANP\triangle ANP also have the radius rr. Prove that AP⋅MP=BP⋅NPAP\cdot MP=BP\cdot NP
geometry