MathDB

ABCDEF

be a convex hexagon which has an inscribed circle and a circumcribed. Denote by

\omega_{A}, \omega_{B},\omega_{C},\omega_{D},\omega_{E}

and

\omega_{F}

the inscribed circles of the triangles

FAB, ABC, BCD, CDE, DEF

and

EFA

, respecitively. Let

l_{AB}

, be the external of

\omega_{A}

and

\omega_{B}

; lines

l_{BC}

l_{CD}

l_{DE}

l_{EF}

l_{FA}

are analoguosly defined. Let

A_1

be the intersection point of the lines

l_{FA}

and

l_{AB}

B_1, C_1, D_1, E_1, F_1

are analogously defined. Prove that

A_1D_1, B_1E_1, C_1F_1

are concurrent.

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