2000 Pan African MO Problems/Problem 5
Let be circle and let be a point outside . Let and be the tangents from to (where ). A line passing through intersects at points and . Let be a point on such that . Prove that bisects .
There is a projective transformation which maps to a circle and that maps the midpoint of to its center (EXPAND); therefore, we may assume without loss of generality that the midpoint of is the center of . But then is the reflection of across , so that is the antipode of on , and we are done.
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