AQ=CD

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Let PA and PB are tangents from a point P to the circle k. From A is drawn a line that intersects k and the segment PB at the points C and D respectively. From B is drawn a line parallel to CD that intersects k at point E. Q is the intersection point of AD and PE. Prove that AQ=CD.

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You can see two solutions here:
http://www.artofproblemsolving.com/Foru ... 0#p2460170