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locus of projections of a fixed point on a line / plane created by perp. rays

Source: Sharygin 2006 CR 24 (a) IX-X (b) X-XI

August 26, 2019
geometryLocus3D geometryprojectionsPlanecirclesphere

Problem Statement

a) Two perpendicular rays are drawn through a fixed point PP inside a given circle, intersecting the circle at points AA and BB. Find the geometric locus of the projections of PP on the lines ABAB. b) Three pairwise perpendicular rays passing through the fixed point PP inside a given sphere intersect the sphere at points A,B,CA, B, C. Find the geometrical locus of the projections PP on the ABCABC plane
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