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Pyramid geometry

Source: St Petersburg Olympiad 2010, Grade 11, P5

September 14, 2017
geometry3D geometrypyramid

Problem Statement

SABCDSABCD is quadrangular pyramid. Lateral faces are acute triangles with orthocenters lying in one plane. ABCDABCD is base of pyramid and ACAC and BDBD intersects at PP, where SPSP is height of pyramid. Prove that AC⊥BDAC \perp BD
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