MathDB

Two Circles - Nordic Math Contest

Source: Nordic Mathematical Contest, April 2005, problem 4.

April 11, 2005

geometrygeometric transformationhomothetyLaTeXgeometry proposed

Problem Statement

The circle

\zeta_{1}

is inside the circle

\zeta_{2}

, and the circles touch each other at

A

. A line through

A

intersects

\zeta_{1}

also at

B

, and

\zeta_{2}

also at

C

. The tangent to

\zeta_{1}

at

B

intersects

\zeta_{2}

at

D

and

E

. The tangents of

\zeta_{1}

passing thorugh

C

touch

\zeta_{2}

at

F

and

G

. Prove that

D

,

E

,

F

and

G

are concyclic.

Back to Problems View on AoPS