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concyclic wanted, 2 circles internally tangent

Source: Switzerland - Swiss MO 2006 p5

July 18, 2020

geometryConcycliccircles

Problem Statement

A circle

k_1

lies within a second circle

k_2

and touches it at point

A

. A line through

A

intersects

k_1

again in

B

and

k_2

in

C

. The tangent to

k_1

through

B

intersects

k_2

at points

D

and

E

. The tangents at

k_1

passing through

C

intersects

k_1

in points

F

and

G

. Prove that

D, E, F

and

G

lie on a circle.

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