MathDB

Incenters of incenters

Source: 2021 Israel TST Test 6 P3

July 25, 2022

geometryincentercircumcircle

Problem Statement

In an inscribed quadrilateral

ABCD

, we have

BC=CD

but

AB\neq AD

. Points

I

and

J

are the incenters of triangles

ABC

and

ACD

respectively. Point

K

was chosen on segment

AC

so that

IK=JK

. Points

M

and

N

are the incenters of triangles

AIK

and

AJK

. Prove that the perpendicular to

CD

at

D

and the perpendicular to

KI

at

I

intersect on the circumcircle of

MAN

.

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