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KA \cdot YB = XA \cdot MB = LA\cdot LB \ne 0 , geometry

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1996 p4

February 20, 2020
geometryProductangles

Problem Statement

Points AA and BB on the rays CXCX and CYCY respectively of an acute angle XCYXCY are given so that CX<CA=CB<CYCX < CA = CB < CY. Construct a line meeting the ray CXCX and the segments AB,BCAB,BC at K,L,MK,L,M, respectively, such that KA⋅YB=XA⋅MB=LA⋅LB≠0KA \cdot YB = XA \cdot MB = LA\cdot LB \ne 0.
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