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< APB + < CPD = 180^o , sphere inscirbed in pyramid with convex ABCD as base

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2008 Seniors p4

September 7, 2020
geometry3D geometryspherepyramidChampions Tournament

Problem Statement

Given a quadrangular pyramid SABCDSABCD, the basis of which is a convex quadrilateral ABCDABCD. It is known that the pyramid can be tangent to a sphere. Let PP be the point of contact of this sphere with the base ABCDABCD. Prove that ∠APB+∠CPD=180o\angle APB + \angle CPD = 180^o.
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