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Another geometry

Source: St Petersburg Olympiad 2009, Grade 10, P7

August 30, 2017

geometrycircumcircle

Problem Statement

Points

Y,X

lies on

AB,BC

of

\triangle ABC

and

X,Y,A,C

are concyclic.

AX

and

CY

intersect in

O

. Points

M,N

are midpoints of

AC

and

XY

. Prove, that

BO

is tangent to circumcircle of

\triangle MON

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