# Centroid, Incentre, Orthocentre?

Geometry Level 5

As shown above, an angle bisector, median, and altitude intersect at the same point in right triangle $$ABC.$$

$$\cos^2 \angle ABC = \dfrac{p}{q+\sqrt{r}},$$ where $$p$$ and $$q$$ are positive integers and $$r$$ is a prime number. Find the value of $$p+q+r$$.

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