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Weird cyclic quadrilateral to prove

Source: Bulgarian Spring Tournament 2023 9.2

March 25, 2023

geometry

Problem Statement

Given is triangle

ABC

with angle bisector

CL

and the

C-

median meets the circumcircle

\Gamma

at

D

. If

K

is the midpoint of arc

ACB

and

P

is the symmetric point of

L

with respect to the tangent at

K

to

\Gamma

, then prove that

DLCP

is cyclic.

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