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5

Part of 2010 Oral Moscow Geometry Olympiad

Problems(2)

angle chasing inside a square ABCD, ML = KL given

Source: 2010 Oral Moscow Geometry Olympiad grades 8-9 p5

8/16/2020
Points KK and MM are taken on the sides ABAB and CDCD of square ABCDABCD, respectively, and on the diagonal ACAC - point LL such that ML=KLML = KL. Let PP be the intersection point of the segments MKMK and BDBD. Find the angle ∠KPL\angle KPL.
squareanglesequal segments
regular pyramid inscribed in a cylinder

Source: 2010 Oral Moscow Geometry Olympiad grades 10-11 p5

5/8/2020
All edges of a regular right pyramid are equal to 11, and all vertices lie on the side surface of a (infinite) right circular cylinder of radius RR. Find all possible values of RR.
geometry3D geometrypyramidinscribedcylinder