MathDB

Point

O

is the center of the circumscribed circle of an acute triangle

Abc

. A certain circle passes through the points

B

and

C

and intersects sides

AB

and

AC

of a triangle. On its arc lying inside the triangle, points

D

and

E

are chosen so that the segments

BD

and

CE

pass through the point

O

. Perpendicular

DD_1

AB

side and perpendicular

EE_1

AC

side intersect at

M

. Prove that the points

A

M

and

O

lie on the same straight line.

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