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an right angle

Source: Mathematics Regional Olympiad of Mexico Southeast 2016 P6

October 26, 2021

geometrycircumcircle

Problem Statement

Let

P

the midpoint of

\Omega

of an acutangle triangle

ABC

with

AB>BC

. Let

\Omega

the circumcircle of

ABC

. Let

P

the intersection of the tangents to

\Omega

in point

A

and

C

and

S

the intersection of

BP

and

AC

. Let

AD

the altitude of triangle

ABP

with

D

in

BP

and

\omega

the circumcircle of triangle

CSD

. Let

K

and

C

the intersections of

\omega

and

\Omega (K\neq C)

. Prove that

\angle CKM=90^\circ

.

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