MathDB

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

Source: Spanish Mathematical Olympiad 1994 P2

July 31, 2018

geometryCircumcentersphere3-Dimensional GeometryLocus3D geometry

Problem Statement

Let

Oxyz

be a trihedron whose edges

x,y, z

are mutually perpendicular. Let

C

be the point on the ray

z

with

OC = c

. Points

P

and

Q

vary on the rays

x

and

y

respectively in such a way that

OP+OQ = k

is constant. For every

P

and

Q

, the circumcenter of the sphere through

O,C,P,Q

is denoted by

W

. Find the locus of the projection of

W

on the plane O

xy

. Also find the locus of points

W