MathDB

2

Part of 1994 Spain Mathematical Olympiad

Problems(1)

locus of projection of a point on plane, locus of circumcenter of sphere

Source: Spanish Mathematical Olympiad 1994 P2

7/31/2018
Let OxyzOxyz be a trihedron whose edges x,y,zx,y, z are mutually perpendicular. Let CC be the point on the ray zz with OC=cOC = c. Points PP and QQ vary on the rays xx and yy respectively in such a way that OP+OQ=kOP+OQ = k is constant. For every PP and QQ, the circumcenter of the sphere through O,C,P,QO,C,P,Q is denoted by WW. Find the locus of the projection of WW on the plane Oxyxy. Also find the locus of points WW.
geometryCircumcentersphere3-Dimensional GeometryLocus3D geometry