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Math Help - Proofs in Plane Geometry

  1. #1
    Member maybeline9216's Avatar
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    Proofs in Plane Geometry

    Please show me how to prove all the sub-parts except part(a).Thanks.
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    Last edited by maybeline9216; October 11th 2008 at 05:55 AM.
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  2. #2
    A riddle wrapped in an enigma
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    Prove: (KF)^2=KN \cdot KC

    This follows easily from \triangle NKF \sim \triangle FKC

    and setting up your corresponding proportional sides:

    \frac{NK}{FK}=\frac{KF}{KC}

    (KF)^2=NK \cdot KC

    Prove: KF=KE

    (KE)^2=KN \cdot KC because a \overline {KE} is a tangent and \overline {KC} is a secant intersecting the circle at N. Justification: Secant-Tangent Theorem.

    Using the previous conclusion and this, we use substitution to obtain:

    (KF)^2=(KE)^2

    KF=KE
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by masters View Post
    Prove: (KF)^2=KN \cdot KC

    This follows easily from \triangle NKF \sim \triangle FKC

    and setting up your corresponding proportional sides:

    \frac{NK}{FK}=\frac{KF}{KC}

    (KF)^2=NK \cdot KC

    Prove: KF=KE

    (KE)^2=KN \cdot KC because a \overline {KE} is a tangent and \overline {KC} is a secant intersecting the circle at N. Justification: Secant-Tangent Theorem.

    Using the previous conclusion and this, we use substitution to obtain:

    (KF)^2=(KE)^2

    KF=KE
    Last Proof: (KE)^2=\frac{1}{4}FN \cdot FA

    (FE)^2=FN \cdot FA by Secant Tangent Theorem

    KF=KE Previously proved

    FE=2(KE)

    Substituting, (2KE)^2=FN \cdot FA

    4(KE)^2=FN \cdot FA

    Q.E.D. (KE)^2=\frac{1}{4}FN \cdot FA
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