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Incenter lies on line

Source: China TST 1 Day 1 Q3

January 2, 2018

geometryTST

Problem Statement

Circle

\omega

is tangent to sides

AB

,

AC

of triangle

ABC

at

D

,

E

respectively, such that

D\neq B

,

E\neq C

and

BD+CE<BC

.

F

,

G

lies on

BC

such that

BF=BD

,

CG=CE

. Let

DG

and

EF

meet at

K

.

L

lies on minor arc

DE

of

\omega

, such that the tangent of

L

to

\omega

is parallel to

BC

. Prove that the incenter of

\triangle ABC

lies on

KL

.

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