MathDB

Let

A_1A_2A_3A_4

be a quadrilateral with no pair of parallel sides. For each

i=1, 2, 3, 4

, define

\omega_1

to be the circle touching the quadrilateral externally, and which is tangent to the lines

A_{i-1}A_i, A_iA_{i+1}

and

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

(indices are considered modulo

4

A_0=A_4, A_5=A_1

and

A_6=A_2

). Let

T_i

be the point of tangency of

\omega_i

with the side

A_iA_{i+1}

. Prove that the lines

A_1A_2, A_3A_4

and

T_2T_4

are concurrent if and only if the lines

A_2A_3, A_4A_1

and

T_1T_3

are concurrent.
Pavel Kozhevnikov, Russia

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