# Triangle Inside The Ellipse

Geometry Level 5

Point $$P(0,1)$$ is on the ellipse $$E: x^2+9y^2=9$$ and point $$A(2,0)$$ lies inside $$E$$. A line passing through $$A$$ meets $$E$$ at points $$B$$ and $$C$$.

If $$\angle{BPC}=90^\circ$$, then the area of triangle $$BPC$$ can be written in the form $$\dfrac{m\sqrt{n}}{p}$$, where $$m,n$$ and $$p$$ are positive integers with $$n$$ square-free and $$m,p$$ coprime. Find $$m+n+p$$.

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