# 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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