SEAMO 2027 - Paper E - SET 03 - Self-study Question 9

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

Practice convention: write the ratio m:n in lowest terms with positive integers m,n. The source omits this convention.



Enter the number only.