Thursday, December 4, 2014

Geometry Problem 1066: Triangle, Obtuse Angle, Orthocenter, Circumradius, Inradius, Exradius, Distance, Diameter

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Online Math: Geometry Problem 1066: Triangle, Obtuse Angle, Orthocenter, Circumradius, Inradius, Exradius, Distance, Diameter.
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1 comment:

  1. Jacob HA (EMK2000)December 4, 2014 at 4:00 PM

    Since ΔABC and ΔHBC have the same circumradius,
    a₁ = 2R cosH = −2R cosA
    r = 4R sin(A/2) sin(B/2) sin(C/2)
    r₁ = 4R sin(A/2) cos(B/2) cos(C/2)

    r₁ − r = 4R sin(A/2) cos(B/2 + C/2)
    = 4R sin²(A/2) = 2R(1−cosA) = 2R + a₁
    a₁ + r₁ − r = 2R
    r₁ − a₁ = 2R + r

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