VMO 1999 Problem 5
OA, OB, OC, OD are 4 rays in space such that the angle between any two is the same. Show that for a variable ray OX, the sum of the cosines of the angles XOA, XOB, XOC, XOD is constant and the sum of the squares of the cosines is also constant.
Community text Kalva (prase.cz mirror). Quoted with source.
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