# ABC problem?

Geometry Level 4

In $$\triangle ABC$$, we have $$AB \times AC=BC^2-AB^2$$. If $$\angle ABC=\theta$$ radians, it follows that $$\angle BCA=\dfrac{p\pi-q\theta}{r}$$ radians, where $$p$$, $$q$$ and $$r$$ are positive integers. What is the minimum possible value of $$p+q+r$$?

×