VTMO 2026 - Grade 9 - Final - SET 4 - Self-study Question 1

Let $ABCD$ be a square and consider the circle with centre $A$ and radius $AB$. Let $M$ be any point on $BC$. A tangent through $M$ to this circle meets $CD$ at $N$.

a) When $MB=MC$, find $NC:ND$.

b) Prove that as $M$ varies, the circumcentre of triangle $AMN$ lies on a fixed straight line.