Question 105
Let $P$ be the intersection point of the diagonals of inscribed quadrilateral $ABCD$. Points $K$ and $L$ are marked on the bisectors of $\angle APD$ and $\angle BPC$, respectively, so that $AP = PK$ and $BP = PL$. Let $M$ be the intersection point of the lines $AK$ and $BL$, and $N$ be the intersection point of the lines $KD$ and $LC$.
Prove that the lines $KL$ and $MN$ are perpendicular.
(D. Pirshtuk)
Prove that the lines $KL$ and $MN$ are perpendicular.
(D. Pirshtuk)