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Triangles $MAB$ and $MA_1B_1$ are similar and have the same orientation

Source: Moldova TST 1994

August 8, 2023

geometrycircumcircle

Problem Statement

Triangles

MAB{}

and

MA_1B_1{}

are similar and have the same orientation. Prove that the circumcircles of these triangles cointain the intersection point of lines

AA_1{}

and

BB_1{}