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line AB bisects the segment PQ, circle related

Source: Switzerland - Swiss TST 1998 p5

February 19, 2020
geometrybisects segmentcircle

Problem Statement

Points AA and BB are chosen on a circle kk. Let AP and BQBQ be segments of the same length tangent to kk, drawn on different sides of line ABAB. Prove that the line ABAB bisects the segment PQPQ.