Problem of the Week 1015

Playing the Angles

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Given an angle theta formed by AOX and point B on OA, let P be the point on the ray OX that subtends the largest angle at AB. For which angle theta is P farthest from O?

Source: Mathematical Diamonds by Ross Honsberger. This is a variation on a famous problem of Regiomontanus that is much used in calculus classes, in which one wishes to determine the optimal place to stand to view a picture on the wall. That corresponds to AOX forming a right angle.

© Copyright 2004 Stan Wagon. Reproduced with permission.