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Coaxal Circles

Source: Turkey TST 2001 - P2

April 4, 2013
geometrygeometric transformationreflectiongeometry proposed

Problem Statement

A circle touches to diameter ABAB of a unit circle with center OO at TT where OT>1OT>1. These circles intersect at two different points CC and DD. The circle through OO, DD, and CC meet the line ABAB at PP different from OO. Show that ∣PA∣⋅∣PB∣=∣PT∣2∣OT∣2.|PA|\cdot |PB| = \dfrac {|PT|^2}{|OT|^2}.
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