MathDB

Let two circles

A

and

B

with unequal radii

r

and

R

, respectively, be tangent internally at the point

A_0

. If there exists a sequence of distinct circles

(C_n)

such that each circle is tangent to both

A

and

B

, and each circle

C_{n+1}

touches circle

C_{n}

at the point

A_n

, prove that

\sum_{n=1}^{\infty} |A_{n+1}A_n| < \frac{4 \pi Rr}{R+r}.

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