MathDB

ASU 575 Commonwealth of Independent States 1991 BP·BQ indepedent plane

Source:

August 15, 2019

3D geometrygeometryPlanefixedProductsphere

Problem Statement

A plane intersects a sphere in a circle

C

. The points

A

and

B

lie on the sphere on opposite sides of the plane. The line joining

A

to the center of the sphere is normal to the plane. Another plane

p

intersects the segment

AB

and meets

C

P

and

Q

. Show that

BP\cdot BQ

is independent of the choice of

p