MathDB

IMOC 2020 G4 concyclic wanted, incenter related

Source: https://artofproblemsolving.com/community/c6h2254883p17398793

September 1, 2020

geometryconicsincenter

Problem Statement

Let

I

be the incenter of triangle

ABC

. Let

BI

and

AC

intersect at

E

, and

CI

and

AB

intersect at

F

. Suppose that

R

is another intersection of

\odot (ABC)

and

\odot (AEF)

. Let

M

be the midpoint of

BC

, and

P, Q

are the intersections of

AI, MI

and

EF

, respectively. Show that

A, P, Q, R

are concyclic.
(ltf0501).