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Triangular Pyramid Problem

Source: 1993 National High School Mathematics League, Exam One, Problem 13

February 28, 2020
geometry3D geometrypyramid

Problem Statement

In triangular pyramid S−ABCS-ABC, any two of SA,SB,SCSA,SB,SC are perpendicular. MM is the centre of gravity of △ABC\triangle ABC. DD is the midpoint of ABAB, line DP//SCDP//SC. Prove: (a) DPDP and SMSM intersect. (b) DP∩SM=D′DP\cap SM=D', then D′D' is the center of circumsphere of S−ABCS-ABC.
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