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Two lines concurrent of the external angle bisector.

Source: St. Petersburg MO 2000, 9th grade, P6

April 22, 2023

geometryangle bisector

Problem Statement

Excircle of

ABC

is tangent to the side

BC

at point

K

and is tangent to the extension of

AB

at point

L

. Another excircle is tangent to extensions of sides

AB

and

BC

at points

M

and

N

. Lines

KL

and

MN

intersect at point

X

. Prove that

CX

is the bisector of angle

ACN

.
[I]Proposed by S. Berlov