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a segment construction, passing through intersections of two circles

Source: Switzerland - Swiss TST 2000 p9

February 19, 2020
intersecting circlesgeometric constructionconstructiongeometrySegmentmax

Problem Statement

Two given circles k1k_1 and k2k_2 intersect at points PP and QQ. Construct a segment ABAB through PP with the endpoints at k1k_1 and k2k_2 for which AP⋅PBAP \cdot PB is maximal.
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