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.
Thursday, October 2, 2008
Elearn Geometry Problem 186
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PROOF of PROBLEM 186
ReplyDeleteM – 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