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Concyclic points from mixtilinear circle

Source: Romanian 2018 TST Day 1 Problem 2

May 25, 2020

geometrymixtilinear incircleincentercircumcircle

Problem Statement

Let

ABC

be a triangle, let

I

be its incenter, let

\Omega

be its circumcircle, and let

\omega

be the

A

- mixtilinear incircle. Let

D,E

and

T

be the intersections of

\omega

and

AB,AC

and

\Omega

, respectively, let the line

IT

cross

\omega

again at

P

, and let lines

PD

and

PE

cross the line

BC

at

M

and

N

respectively. Prove that points

D,E,M,N

are concyclic. What is the center of this circle?

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