Monday, November 3, 2008

Elearn Geometry Problem 200: Right Triangle, Incircle, Excircles

Triangle, Altitude, Angles

See complete Problem 200 at:
www.gogeometry.com/problem/p200_right_triangle_tangent.htm

Right Triangle, Incircle, Excircles, Points of Tangency, Inradius. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

1 comment:

  1. inradius in right triangle is r = (a + b - c )/2
    in this case

    r = ( b + c - a )/2 => r = b/2 + c/2 - a/2 (a,hypothe)
    r = b/2 + c/2 + a/2 - a/2 - a/2 ( add & subtract a/2 )
    r = (b + c + a)/2 - (a/2 + a/2)

    r = s - a
    -----------------------------------------------------
    name K small circle meet BC, L medium circle meet AC
    T big circle meet BA

    FC = LC ( tang from C )
    FB + BK + KC = LA + r + EC
    FB + BK = AH + r (KC = EC tg from C,LA = AH tg from A)
    FB + BH + HD = AD + HD + r
    FB + FB = r + r ( BH = FB tg from B, AD = r)
    2 FB = 2r

    FB = r
    ----------------------------------------------------
    BG = BT ( tg from B)
    a + CG = AB + AT
    a + CG = c + b - CM (AB = c, AT = AM = b - CM)
    2CG = c + b - a
    2CG = BD + r + EC + r - BD - EC (c=BD+r,b=EC+r,a=BD+EC
    2CG = 2r

    CG = r
    --------------------------------------------------
    ADOE is square ( 4 angle = 90°, 2 side by side equal)

    -----------------------------------------------------

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