11.6

Part of 2005 Sharygin Geometry Olympiad

Problems(1)

lines intersect on the inscribed sphere on a tetrahedron, concurrency

Source: Sharygin 2005 finals 11.6

The sphere inscribed in the tetrahedron

ABCD

touches its faces at points

A',B',C',D'

AA'

BB'

intersect, and the point of their intersection lies on the inscribed sphere. Prove that the segments

CC'

DD'

also intersect on the inscribed sphere.

geometry3D geometrytetrahedronsphereconcurrencyconcurrent