# Intelligent Orthocenter

Geometry Level 4

In a triangle $$ABC$$, if the altitude drawn from vertex $$A$$ meets the circumcircle at a point $$P=(1,5)$$ and the equation of the side $$BC$$ is, $$x + y + 4 = 0.$$ Then the orthocenter, $$H$$ is $$(a,b)$$. Find $$|a+b|$$.

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