Question 89
On a line $l$ there are three different points $A$, $B$ and $P$ in that order. Let $a$ be the line through $A$ perpendicular to $l$, and let $b$ be the line through $B$ perpendicular to $l$. A line through $P$, not coinciding with $l$, intersects $a$ in $Q$ and $b$ in $R$. The line through $A$ perpendicular to $B Q$ intersects $B Q$ in $L$ and $B R$ in $T$. The line through $B$ perpendicular to $A R$ intersects $A R$ in $K$ and $A Q$ in $S$.
a. Prove that $P$, $T$, $S$ are collinear.
b. Prove that $P$, $K$, $L$ are collinear.
a. Prove that $P$, $T$, $S$ are collinear.
b. Prove that $P$, $K$, $L$ are collinear.