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3 lines in space passing through a point ...

Source: 1st Mexican Mathematical Olympiad 1987 OMM P8

July 27, 2018
geometry3-Dimensional Geometrysolid geometryperpendicular

Problem Statement

(a) Three lines l,m,nl,m,n in space pass through point SS. A plane perpendicular to mm intersects l,m,nl,m,n at A,B,CA,B,C respectively. Suppose that ∠ASB=∠BSC=45o\angle ASB = \angle BSC = 45^o and ∠ABC=90o\angle ABC = 90^o. Compute ∠ASC\angle ASC. (b) Furthermore, if a plane perpendicular to ll intersects l,m,nl,m,n at P,Q,RP,Q,R respectively and SP=1SP = 1, find the sides of triangle PQRPQR.
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