MathDB
2007 Guts #16: Triangles and Parallel Lines

Source:

June 22, 2012
geometry

Problem Statement

Let ABCABC be a triangle with AB=7AB=7, BC=9BC=9, and CA=4CA=4. Let DD be the point such that AB∥CDAB\parallel CD and CA∥BDCA\parallel BD. Let RR be a point within triangle BCDBCD. Lines ℓ\ell and mm going through RR are parallel to CACA and ABAB respectively. Line ℓ\ell meets ABAB and BCBC at PP and P′P^\prime respectively, and mm meets CACA and BCBC at QQ and Q′Q^\prime respectively. If SS denotes the largest possible sum of the areas of triangle BPP′BPP^\prime, RP′Q′RP^\prime Q^\prime, and CQQ′CQQ^\prime, determine the value of S2S^2.
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