MathDB

Geometry

Source: Polish MO

February 25, 2017

geometrycircumcircle

Problem Statement

Incircle of a triangle

ABC

touches

AB

and

AC

at

D

and

E

, respectively. Point

J

is the excenter of

A

. Points

M

and

N

are midpoints of

JD

and

JE

. Lines

BM

and

CN

cross at point

P

. Prove that

P

lies on the circumcircle of

ABC

.

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