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C_1,C_2 are incircle,circumcircle of triangle A'B'C' besides triangle ABC

Source: Estonia IMO TST 2001 p6

March 26, 2020

incirclecircumcirclegeometry

Problem Statement

Let

C_1

and

C_2

be the incircle and the circumcircle of the triangle

ABC

, respectively. Prove that, for any point

A'

C_2

, there exist points

B'

and

C'

such that

C_1

and

C_2

are the incircle and the circumcircle of triangle

A'B'C'

, respectively.