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Common tangents of circumcircle and excircle

Source: Brazilian Olympic Revenge 2020, P3

February 1, 2020

geometrycircumcircleBrazilolympic revenge

Problem Statement

Let

ABC

be a triangle and

\omega

its circumcircle. Let

D

and

E

be the feet of the angle bisectors relative to

B

and

C

, respectively. The line

DE

meets

\omega

at

F

and

G

. Prove that the tangents to

\omega

through

F

and

G

are tangents to the excircle of

\triangle ABC

opposite to

A

.

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