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Plane passes through a fixed point [Iran Second Round 1989]

Source:

December 6, 2010
geometry3D geometryspheregeometry proposed

Problem Statement

A sphere SS with center OO and radius RR is given. Let PP be a fixed point on this sphere. Points A,B,CA,B,C move on the sphere SS such that we have ∠APB=∠BPC=∠CPA=90∘.\angle APB = \angle BPC = \angle CPA = 90^\circ. Prove that the plane of triangle ABCABC passes through a fixed point.
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