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Sphere geometry

Source: Sharygin geometry olympiad 2015, grade 10, Final Round, Problem 7

July 17, 2018
geometry3D geometrysphere

Problem Statement

Let SABCDSABCD be an inscribed pyramid, and AA1AA_1, BB1BB_1, CC1CC_1, DD1DD_1 be the perpendiculars from AA, BB, CC, DD to lines SCSC, SDSD, SASA, SBSB respectively. Points SS, A1A_1, B1B_1, C1C_1, D1D_1 are distinct and lie on a sphere. Prove that points A1A_1, B1B_1, C1C_1 and D1D_1 are coplanar.
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