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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