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Putnam 1949 A4

Source: Putnam 1949

March 20, 2022
Putnamgeometry3D geometrytetrahedron

Problem Statement

Given that PP is a point inside a tetrahedron with vertices at A,B,CA, B, C and DD, such that the sum of the distances PA+PB+PC+PDPA+PB+PC+PD is a minimum, show that the two angles ∠APB\angle APB and ∠CPD\angle CPD are equal and are bisected by the same straight line. What other pair of angles must be equal?
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