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A geometry about concyclic points

Source: Turkey EGMO TST 2020 #5

July 15, 2020

geometrygeometry proposed

Problem Statement

A, B, C, D, E

points are on

\Gamma

cycle clockwise.

[AE \cap [CD = \{M\}

and

[AB \cap [DC = \{N\}

. The line parallels to

EC

and passes through

M

intersects with the line parallels to

BC

and passes through

N

on

K

. Similarly, the line parallels to

ED

and passes through

M

intersects with the line parallels to

BD

and passes through

N

on

L

. Show that the lines

LD

and

KC

intersect on

\Gamma

.

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