Intelligent Orthocenter

Geometry Level pending

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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