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circle having the line segment KL as diameter passes through O

Source: Norwegian Mathematical Olympiad 2002 - Abel Competition p3a

February 21, 2020
geometryTangentscircle

Problem Statement

A circle with center in OO is given. Two parallel tangents tangent to the circle at points MM and NN. Another tangent intersects the first two tangents at points KK and LL. Show that the circle having the line segment KLKL as diameter passes through OO.
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