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Math Help - Proof: An Isosceles Triangle inscribed in a Circle

  1. #1
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    Proof: An Isosceles Triangle inscribed in a Circle


    Hypothesis: AC = CB
    DE is the diameter
    CH is perpendicular to AB (the altitude)
    Thesis: DE : BC = BC : CH (BC^2 = DE * CH)
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Proof: An Isosceles Triangle inscribed in a Circle

    Quote Originally Posted by goby View Post

    Hypothesis: AC = CB
    DE is the diameter
    CH is perpendicular to AB (the altitude)
    Thesis: DE : BC = BC : CH (BC^2 = DE * CH)
    A=\frac{1}{2} *AB*CH

    R=\frac{AB*BC*CA}{4A} (Circumradius - AoPSWiki)

    R=\frac{AB*BC*CA}{4*\frac{1}{2}*AB*CH}

    R=\frac{BC*CA}{2CH}

    R=\frac{BC^2}{2CH}

    \frac{BC^2}{CH}=2R=DE

    BC^2=DE*CH
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    Re: Proof: An Isosceles Triangle inscribed in a Circle

    Okay, I understood it, but what's the proof for R = ?
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    MHF Contributor alexmahone's Avatar
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    Re: Proof: An Isosceles Triangle inscribed in a Circle

    Quote Originally Posted by goby View Post
    Okay, I understood it, but what's the proof for R = ?
    Area of a Triangle in Terms of Circumradius - ProofWiki
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