MathDB

Two circles inside another circle

Source: Baltic Way 1992 #19

February 18, 2009

geometryangle bisectorgeometry proposed

Problem Statement

Let

C

be a circle in plane. Let

C_1

and

C_2

be nonintersecting circles touching

C

internally at points

A

and

B

respectively. Let

t

be a common tangent of

C_1

and

C_2

touching them at points

D

and

E

respectively, such that both

C_1

and

C_2

are on the same side of

t

. Let

F

be the point of intersection of

AD

and

BE

. Show that

F

lies on

C

.

Back to Problems View on AoPS