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As shown above, an angle bisector, median, and altitude intersect at the same point in right triangle ABC.ABC.ABC.
cos2∠ABC=pq+r,\cos^2 \angle ABC = \dfrac{p}{q+\sqrt{r}},cos2∠ABC=q+rp, where ppp and qqq are positive integers and rrr is a prime number. Find the value of p+q+rp+q+rp+q+r.
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