Question 15
Given a circle $c$ and two fixed points $A$, $B$ on it. $M$ is another point on $c$, and $K$ is the midpoint of $BM$. $P$ is the foot of the perpendicular from $K$ to $AM$.
a. Prove that $KP$ passes through a fixed point (as $M$ varies).
b. Find the locus of $P$.
a. Prove that $KP$ passes through a fixed point (as $M$ varies).
b. Find the locus of $P$.