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A line, a median and a bisector have a common point

Source: Tuymaada 2014, Day 2, Problem 3, Senior League

July 12, 2014

geometryparallelogramincenteranalytic geometrygeometry unsolvedTuymaada

Problem Statement

A parallelogram

ABCD

is given. The excircle of triangle

\triangle{ABC}

touches the sides

AB

at

L

and the extension of

BC

at

K

. The line

DK

meets the diagonal

AC

at point

X

; the line

BX

meets the median

CC_1

of trianlge

\triangle{ABC}

at

{Y}

. Prove that the line

YL

, median

BB_1

of triangle

\triangle{ABC}

and its bisector

CC^\prime

have a common point.
(A. Golovanov)

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