MathDB

MMC 2012 problem 4

Source:

June 23, 2013

geometrycircumcirclegeometry proposed

Problem Statement

Let

O

be the circumcenter,

R

be the circumradius, and

k

be the circumcircle of a triangle

ABC

. Let

AB

be a circle tangent to the rays

AB

and

AC

, and also internally tangent to

k

. Let

A_2

be a circle tangent to the rays

k_1

and

AC

, and also externally tangent to

k

. Let

A_1

and

A_2

denote the respective centers of

k_1

and

k_2

. Prove that:

(OA_1+OA_2)^2-A_1A_2^2 = 4R^2.

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