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A sphere is inscribed in tetrahedron ABCD

Source: Polish MO Round 3 2009 problem 5

November 3, 2009
geometry3D geometryspheretetrahedroncircumcirclegeometry unsolved

Problem Statement

A sphere is inscribed in tetrahedron ABCD ABCD and is tangent to faces BCD,CAD,ABD,ABC BCD,CAD,ABD,ABC at points P,Q,R,S P,Q,R,S respectively. Segment PT PT is the sphere's diameter, and lines TA,TQ,TR,TS TA,TQ,TR,TS meet the plane BCD BCD at points A′,Q′,R′,S′ A',Q',R',S'. respectively. Show that A A is the center of a circumcircle on the triangle S′Q′R′ S'Q'R'.
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