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<O_1DM = <ODO_2 -- 2011 Cuba MO 2.6

Source:

September 18, 2024

geometryequal sngles

Problem Statement

Let

ABC

be a triangle with circumcenter

\omega (O_2)

. Let

\omega (O_1)

be the circumference which passes through

C

and

BC

and is tangent to

BC

at

M

.

O_1O_2

the circle that passes through

A

and

C

and is tangent to

BC

at

C

. Let

M

the midpoint of

O_1O_2

and

D

the symmetric point of

O

with respect to

A

. Prove that

\angle O_1DM = \angle ODO_2

.

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