MathDB

Tangent Circles

Source: Azerbaijan IMO TST 2016,D1 P1

May 26, 2018

geometrycircumcircle

Problem Statement

Tangents from the point

A

to the circle

\Gamma

touche this circle at

C

and

D

.Let

AD

be a point on

\Gamma

,different from

C

and

D

. The circle

\omega

that passes through points

A

and

B

intersect with lines

AC

and

E

at

F

and

E

,respectively.Prove that the circumcircles of triangles

ABC

and

DEB

are tangent if and only if the points

C,D,F

and

E

are cyclic.

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