SEAMO 2023 — Paper E — Grade 9–10 Question 23

In triangle $ABC$, $\angle A=90^\circ$, $AB=AC$, and $M$ is the midpoint of $AC$. The line $AD\perp BM$ meets $BC$ at $D$. If $\angle AMB:\angle CMD=m:n$ in lowest terms, find $m+n$.