Thursday, October 2, 2008

Elearn Geometry Problem 186

Right Triangle, Altitude, Incenter

See complete Problem 186 at:
www.gogeometry.com/problem/p186_right_triangle_circle.htm

Right Triangle, Altitude, Incenters, Circles. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

1 comment:

  1. PROOF of PROBLEM 186
    M – tangency point on BC, K - tangency point on BD
    angleDBC=angleBAD=α→
    angleDBF=angleEAD=∝/2→
    angleADE=angleBDF=45°→
    ∆AED≈∆BFD→ ED/DF=AD/BD,angleEDF=angleADB=90°→∆ABD≈∆EFD→angleEFD=β
    angleBFE=180°-β-∝/2-45°= ∝/2+angleBGF→
    angleBGF=45°,
    angleFKB=angleFMG=90°→MG=KD=R→
    BM=BK,BG=BM+R=BK+R=BD

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