MathDB

6 points concyclic wanted, incircle and incenter related

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist G3 day2

September 25, 2021

geometryincenterConcyclic

Problem Statement

Let

\vartriangle ABC

be acute, with incircle

\Gamma

and incenter

I

\Gamma

touches sides

AB

BC

and

AC

Z

X

and

Y

, respectively. Let

D

be the intersection of

XZ

with

CI

and

L

the intersection of

BI

with

XY

. Suppose

D

and

L

are outside of

\vartriangle ABC

. Prove that

A

D

Z

I

Y

, and

L

lie on a circle.