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Problem 12.2

Part of 2007 Bulgarian Autumn Math Competition

Problems(1)

Intersection of plane and a pyramid is a trapezoid

Source: 2007 Bulgarian Autumn Math Competition, Problem 12.2

3/17/2022
All edges of the triangular pyramid ABCDABCD are equal in length. Let MM be the midpoint of DBDB, NN is the point on AB‾\overline{AB}, such that 2NA=NB2NA=NB and N∉ABN\not\in AB and PP is a point on the altitude through point DD in △BCD\triangle BCD. Find ∠MPD\angle MPD if the intersection of the pyramid with the plane (NMP)(NMP) is a trapezoid.
3D geometrygeometrypyramidtrapezoidPlane