Question 153
A triangle $ABC$ is given. Circle $k$ touches $\overline{BC}$ from outside the triangle at point $K$, and the extensions of lines $\overline{AB}$ and $\overline{AC}$ over points $B$ and $C$ at points $L$ and $M$, respectively. The circle with diameter $\overline{BC}$ intersects segment $LM$ at points $P$ and $Q$ so that point $P$ lies between $L$ and $Q$.
Prove that lines $BP$ and $CQ$ intersect at the centre of circle $k$.
(Stipe Vidak)
Prove that lines $BP$ and $CQ$ intersect at the centre of circle $k$.
(Stipe Vidak)