# Trigonometry/Circles and Triangles/Philo's Line

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.