IMC 2002 — Keystage 3 (IWYMIC) — individual Question 12

In triangle $ABC$, $\angle CAB=36^\circ$, $\angle BCA=72^\circ$. Let $D$ lie on $AC$ such that $BD$ bisects $\angle ABC$. Let $E$ lie on $AB$ with $CE\perp BD$. How many isosceles triangles are in the diagram?