MathDB

575

Part of 1992 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

8/15/2019
A plane intersects a sphere in a circle CC. The points AA and BB lie on the sphere on opposite sides of the plane. The line joining AA to the center of the sphere is normal to the plane. Another plane pp intersects the segment ABAB and meets CC at PP and QQ. Show that BPā‹…BQBP\cdot BQ is independent of the choice of pp.
3D geometrygeometryPlanefixedProductsphere