MathDB

Two circles

c

and

d

are situated in the plane each outside the other. The points

C

and

D

are located on circles

c

and

d

respectively, so as to be as far apart as possible. Two smaller circles are constructed inside

c

and

d

. Of these the first circle touches

c

and the two tangents drawn from

C

d

, while the second circle touches

d

and the two tangents from

D

c

. Prove that the small circles are equal.
(J. Tabov, Sofia)

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