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Pyramid base

Source: St Petersburg Olympiad 2012, Grade 11, P3

September 29, 2017
geometry3D geometrypyramid

Problem Statement

At the base of the pyramid SABCDSABCD lies a convex quadrilateral ABCDABCD, such that BC∗AD=BD∗ACBC * AD = BD * AC. Also ∠ADS=∠BDS,∠ACS=∠BCS \angle ADS =\angle BDS ,\angle ACS =\angle BCS. Prove that the plane SABSAB is perpendicular to the plane of the base.
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