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distance of projection of a point on a plane from another plane

Source: 1997 Romania NMO VIII p4

August 13, 2024
geometry3D geometrydistance

Problem Statement

Let SS be a point outside of the plane of the parallelogram ABCDABCD, such that the triangles SABSAB, SBCSBC, SCDSCD and SADSAD are equivalent.
a) Prove that ABCDABCD is a rhombus.
b) If the distance from SS to the plane (A,B,C,D)(A, B, C, D) is 1212, BD=30BD = 30 and AC=40AC = 40, compute the distance from the projection of the point SS on the plane (A,B,C,D)(A, B, C, D) to the plane (S,B,C)(S,B,C) .
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