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

Labels:
circle,
proportions,
tangency point,
tangent,
triangle

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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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