MathDB

geometry problem

Source: Netherlands TST for IMO 2017, day 2,problem 2

February 1, 2018

geometry

Problem Statement

The incircle of a non-isosceles triangle

ABC

has centre

I

and is tangent to

BC

and

CA

in

D

and

E

, respectively. Let

H

be the orthocentre of

ABI

, let

K

be the intersection of

AI

and

BH

and let

L

be the intersection of

BI

and

AH

. Show that the circumcircles of

DKH

and

ELH

intersect on the incircle of

ABC

.

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