Thursday, May 13, 2010

Problem 452: Triangle, Circle, Tangent, Proportional Segments

Geometry Problem
Click the figure below to see the complete problem 452 about Triangle, Circle, Tangent, Proportional Segments.

Problem 452: Triangle, Circle, Tangent, Proportional Segments.
See also:
Complete Problem 452
Level: High School, SAT Prep, College geometry

3 comments:

  1. draw FG//AC , G on AB
    BAE = 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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  2. Draw BG//FE with G on AC
    mAGB=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)

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  3. 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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