MathDB

Concurency

Source: Turkey TST 2014 Day 2 Problem 5

March 12, 2014

geometrycircumcirclegeometric transformationhomothetytrigonometryconicsinequalities

Problem Statement

A circle

\omega

cuts the sides

BC,CA,AB

of the triangle

ABC

at

A_1

and

A_2

;

B_1

and

B_2

;

C_1

and

C_2

, respectively. Let

P

be the center of

\omega

.

A'

is the circumcenter of the triangle

A_1A_2P

,

B'

is the circumcenter of the triangle

B_1B_2P

,

C'

is the circumcenter of the triangle

C_1C_2P

. Prove that

AA', BB'

and

CC'

concur.

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