Question 24
A trapezium $ABCD$ is given. The bisector of the leg $\overline{BC}$ intersects the leg $\overline{AD}$ at $M$, while the bisector of $\overline{AD}$ intersects $\overline{BC}$ at $N$.
Let $O_1$ and $O_2$ be the circumcentres of triangles $ABN$ and $CDM$, respectively.
Prove that the line $O_1O_2$ bisects the segment $MN$. (Stipe Vidak)
Let $O_1$ and $O_2$ be the circumcentres of triangles $ABN$ and $CDM$, respectively.
Prove that the line $O_1O_2$ bisects the segment $MN$. (Stipe Vidak)