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Equal angles

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 1

May 31, 2009

geometry proposedgeometry

Problem Statement

Points

B_1

and

B_2

lie on ray

AM

, and points

C_1

and

C_2

lie on ray

AK

. The circle with center

O

is inscribed into triangles

AB_1C_1

and

AB_2C_2

. Prove that the angles

B_1OB_2

and

C_1OC_2

are equal.