Day 22: A Forest of Lines

Geometry Level 4

A triangle \(ABC\) is right angled at \(B\). From each of \(A\) and \(C\) two angle trisectors are drawn to the opposite side, and from each of the four intersections a perpendicular is drawn onto the side \(AC\). The feet of these perpendiculars are named \(M, N, O\) and \(P\) in order from \(A\).

Find the value of \(\angle MBN + \angle OBP\).

This problem is part of the set Advent Calendar 2014.

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