Geometry Problem
Click the figure below to see the complete problem 452 about Triangle, Circle, Tangent, Proportional Segments.
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Complete Problem 452
Level: High School, SAT Prep, College geometry
Thursday, May 13, 2010
Problem 452: Triangle, Circle, Tangent, Proportional Segments
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draw FG//AC , G on AB
ReplyDeleteBAE = FEA => AEFG trapezoid isoceles =>
AG = d, BG = c-d, =>
▲BGF = ▲BAC
from thales theorem
BG/AG = BF/FC =>
(c-d)/d = (c+d)/x (equal segm tg from a points,B, F )
x = d(c+d)/(c-d)
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Draw BG//FE with G on AC
ReplyDeletemAGB=mCEF=mBAG => BG=c
Draw HF//AC with H on BG
consider similar triangles CFE and FBH,
x/d=(c+d)/(c-d) <=>
x=d(c+d)/(c-d)
Parallel of AE through F meets BA at P. <A=<E, so AP=D. BF/BP=(c+d)/(c-d)=sin<BPF/sin<BFP=sin<FEC/sin<BFP=sin<FEC/sin<C=x/d.
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