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PA^2+PB^2=4PT^2

Source: Pan African Olympiad 2008

October 1, 2011
geometry proposedgeometry

Problem Statement

Let C1C_1 be a circle with centre OO, and let ABAB be a chord of the circle that is not a diameter. MM is the midpoint of ABAB. Consider a point TT on the circle C2C_2 with diameter OMOM. The tangent to C2C_2 at the point TT intersects C1C_1 at two points. Let PP be one of these points. Show that PA2+PB2=4PT2PA^2+PB^2=4PT^2.
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