# The Triangle

Level pending

Let $$ABC$$ be a triangle in which $$AB=AC$$. Let $$D$$ be the midpoint of $$BC$$ and $$P$$ be a point on $$AD$$. Suppose $$E$$ be the foot of perpendicular from $$P$$ on $$AC$$. If $$\frac{AP}{PD}=\frac{BP}{PE}=a$$, $$\frac{BD}{AD}=m$$ and $$z=m^2(1+a)$$, Then find the value of $$z^2-(a^3-a^2-2)z+1$$

×