Question 92
Let $ABCD$ be a quadrilateral circumscribed around a circle with center $O$. We construct equal segments $AA_1$, $AA_2$, $CC_1$ and $CC_2$ on rays $AB$, $AD$, $CB$ and $CD$ respectively, so that their lengths are greater than that of any side of $ABCD$, and $A_1$, $A_2$, $C_1$ and $C_2$ are located on the circle with center $O$. Prove that lines $A_1A_2$, $C_1C_2$ and $BD$ either intersect at one point or are parallel.
(Olena Artemchuk, Mykola Moroz)
Fig. 38
(Olena Artemchuk, Mykola Moroz)
Fig. 38