Question 3
Triangle $ABC$ is isosceles at $A$. Points $M,N$ move on the rays opposite to $BA,CA$ respectively, with $CN=2BM$. Point $D$ lies on the segment $MN$ with $DN=2DM$.
a) Prove that $D$ always moves on a fixed line.
b) Let $I,J$ be the midpoints of $BC,MN$ respectively. The line $IJ$ meets the line through $A$ parallel to $BC$ at $K$. Prove that $\angle IKD$ is constant.
a) Prove that $D$ always moves on a fixed line.
b) Let $I,J$ be the midpoints of $BC,MN$ respectively. The line $IJ$ meets the line through $A$ parallel to $BC$ at $K$. Prove that $\angle IKD$ is constant.