See complete Problem 34 at:
www.gogeometry.com/problem/p034_right_triangle_incircle.htm
Right Triangle, Incircles, Inradius, Cevian. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Monday, May 19, 2008
Elearn Geometry Problem 34: Right Triangle
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AE = AG ( tang from A at the same circle are equal )
ReplyDeleteAH = AK
=>
AE - AH = AG - AK
HE = KG (1)
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BL = BM ( tg from B at circle O' )
BJ + JL = BF + FM
BJ + JD - DL = BE + GN ( BF = BE, FM = GN comm ext tg)
BJ + KD - DL = BE + GD + DN ( JD=KD, tg from D )
BE + HE + KD - DL = BE + GD + DN ( BH=BJ, tg from B )
HE + KG + GD = GD + 2∙DN ( DL = DN, tg from D )
2∙KG = 2∙DN ( HE = KG from (1) )
KG = DN (2)
HE = KG = DN
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BEO"F is square ( EO"=O"F=r & ang B = 90°)
BH = r + HE = BJ but ( DL = DN = KG = HE )=>
r = BJ - DL
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