Geometry Problem
Click the figure below to see the complete problem 471 about Triangle, Parallel, Side, Concurrency, Area, Similarity.
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Complete Problem 471
Level: High School, SAT Prep, College geometry
Tuesday, July 13, 2010
Problem 471: Triangle, Parallel, Side, Concurrency, Area, Similarity
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Clearly, triangles FDO, MOE, OHG & BAC are all similar. Hence, S1/S = DO^2/AC^2 = AH^2/AC^2 or √(S1/S)=AH/AC. Likewise,√(S2/S)=OE/AC=GC/AC and √(S3/S)=HG/AC which gives us: √(S1/S)+√(S2/S)+√(S3/S)=(AH+HG+GC)/AC=AC/AC=1. Hence, √S=√S1+√S2+√S3.
ReplyDeleteVihaan