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Trigonometry/Circles and Triangles/Philo's Line

< Trigonometry

Suppose any angle POQ and a point X between the lines OP and OQ. Philo's line is the shortest line AB through X such that A is on OP (or OP produced) and B is on OQ (or OQ produced).

If Y is the foot of the perpendicular from O to AB, then AY = BX.