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Find the maximum value of OM + ON - MN

Source: China Team Selection Test 2004, Day 1, Problem 1

October 13, 2005
LaTeXgeometry unsolvedgeometry

Problem Statement

Let ∠XOY=π2\angle XOY = \frac{\pi}{2}; PP is a point inside ∠XOY\angle XOY and we have OP=1;∠XOP=π6.OP = 1; \angle XOP = \frac{\pi}{6}. A line passes PP intersects the Rays OXOX and OYOY at MM and NN. Find the maximum value of OM+ON−MN.OM + ON - MN.
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