22

Part of 2021 Sharygin Geometry Olympiad

Problems(1)

Point belonging to all balls on a polyhedron

Source: XVII Sharygin Correspondence Round, P22

A convex polyhedron and a point

K

outside it are given. For each point

M

of a polyhedron construct a ball with diameter

MK

. Prove that there exists a unique point on a polyhedron which belongs to all such balls.

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