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Show that angle BMN=90

Source: Moldova TST 2020

March 7, 2020

geometry

Problem Statement

Let

\Delta ABC

be an acute triangle and

\Omega

its circumscribed circle, with diameter

AP

. Points

E

and

F

are the orthogonal projections from

B

on

AC

and

AP

, points

M

and

N

are the midpoints of segments

EF

and

CP

. Prove that

\angle BMN=90

.

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