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Two circles externally tangent again!

Source: Balkan MO 1993, Problem 3

April 25, 2006

geometryincentercircumcirclegeometry proposed

Problem Statement

Circles

\mathcal C_1

and

\mathcal C_2

with centers

O_1

and

O_2

, respectively, are externally tangent at point

\lambda

. A circle

\mathcal C

with center

O

touches

\mathcal C_1

at

A

and

\mathcal C_2

at

B

so that the centers

O_1

,

O_2

lie inside

C

. The common tangent to

\mathcal C_1

and

\mathcal C_2

at

\lambda

intersects the circle

\mathcal C

at

K

and

L

. If

D

is the midpoint of the segment

KL

, show that

\angle O_1OO_2 = \angle ADB

. Greece

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