Question 12
In triangle $ABC$, $AB=12$, $BC=13$ and $AC=15$. Point $P$ lies on $AC$ such that the incircles of triangles $ABP$ and $BCP$ have equal radii.
Let $m,n$ be relatively prime positive integers such that $AP/CP=m/n$. Find $m+n$.
The two incircles are circles of nondegenerate triangles, so $P$ lies strictly between $A$ and $C$.
Let $m,n$ be relatively prime positive integers such that $AP/CP=m/n$. Find $m+n$.
The two incircles are circles of nondegenerate triangles, so $P$ lies strictly between $A$ and $C$.