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Circumcircles are tangent

Source: All russian olympiad 2016,Day2,grade 10,P8

May 1, 2016

geometry

Problem Statement

In acute triangle

ABC

,

AC<BC

,

M

is midpoint of

AB

and

\Omega

is it's circumcircle.Let

CM

be antipode of

C

in

\Omega

.

AC^\prime

and

BC^\prime

intersect with

CM

at

K,L

,respectively.The perpendicular drawn from

K

to

AC^\prime

and perpendicular drawn from

L

to

BC^\prime

intersect with

AB

and each other and form a triangle

\Delta

.Prove that circumcircles of

\Delta

and

\Omega

are tangent.(M.Kungozhin)

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