MathDB
Triangle in a space

Source:

December 9, 2005
geometry3D geometryspheregeometry proposed

Problem Statement

There is given a triangle ABCABC in a space. A sphere does not intersect the plane of ABCABC. There are 44 points K,L,M,PK, L, M, P on the sphere such that AK,BL,CMAK, BL, CM are tangent to the sphere and AKAP=BLBP=CMCP\frac{AK}{AP} = \frac{BL}{BP} = \frac{CM}{CP}. Show that the sphere touches the circumsphere of ABCPABCP.
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