MathDB

ASU 505 All Soviet Union MO 1989 intersecting spheres, equal projections

Source:

August 14, 2019

geometry3D geometrysphereprojection

Problem Statement

S

and

S'

are two intersecting spheres. The line

BXB'

is parallel to the line of centers, where

B

is a point on

S, B'

is a point on

S'

and

X

lies on both spheres.

A

is another point on

S

, and

A'

is another point on S' such that the line

AA'

has a point on both spheres. Show that the segments

AB

and

A'B'

have equal projections on the line

AA'