MathDB

Let

n \geq 5

be integer. The convex polygon

P = A_{1} A_{2} \ldots A_{n}

is bicentric, that is, it has an inscribed and circumscribed circle. Set

A_{i+n}=A_{i}

to every integer

i

(that is, all indices are taken modulo

n

). Suppose that for all

i, 1 \leq i \leq n

, the rays

A_{i-1} A_{i}

and

A_{i+2} A_{i+1}

meet at the point

B_{i}

. Let

\omega_{i}

be the circumcircle of

B_{i} A_{i} A_{i+1}

. Prove that there is a circle tangent to all

n

circles

\omega_{i}

1 \leq i \leq n

Problem Statement