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P Q =// 2 RS wanted, 4 semicircles on a line 2013-14 Dürer Round1 C2

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December 4, 2022
geometrysemicirclesequal segmentsDurer

Problem Statement

Above the segments ABAB and BCBC we drew a semicircle at each. F1F_1 bisects ABAB and F2F_2 bisects BCBC. Above the segments AF2AF_2 and F1CF_1C we also drew a semicircle at each. Segments PQP Q and RSRS touch the corresponding semicircles as shown in the figure. Prove that PQ∥RSP Q \parallel RS and ∣PQ∣=2⋅∣RS∣|P Q| = 2 \cdot |RS|. https://cdn.artofproblemsolving.com/attachments/8/2/570e923b91e9e630e3880a014cc6df4dc33aa2.png
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