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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 do part(c) proving.Thanks alot.
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  2. #2
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    Part c: Prove (BE)^2 = (AB)(BC)

    In right triangle ABE, by Pythagorean theorem,
    (BE)^2 = (AE)^2 -(AB)^2 ----------(1)

    In right triangle CBE,
    (BE)^2 = (EC)^2 -(BC)^2 ----------(2)

    Add (1) and (2),
    2(BE)^2 = [(AE)^2 +(EC)^2] -[(AB)^2 +(BC)^2] ---------(3)

    Since AE is tangent to circle Q, then AE is perpendicular to EC, hence, triangle AEC is a right triangle.
    So,
    (AC)^2 = (AE)^2 +(EC)^2 -----------------(4)
    Substitute that into (3),
    2(BE)^2 = (AC)^2 -[(AB)^2 +(BC)^2] ------(5)

    In the straight line ABC,
    (AC)^2 = (AB +BC)^2
    (AC)^2 = (AB)^2 +2(AB)(BC) +(BC)^2 --------(6)
    Substitute that into (5),
    2(BE)^2 = [(AB)^2 +2(AB)(BC) +(BC)^2] -[(AB)^2 +(BC)^2]
    2(BE)^2 = 2(AB)(BC)
    (BE)^2 = (AB)(BC)

    Proven.
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  3. #3
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    All the best to your GCE O Level A.Maths on next Wednesday.
    Last edited by NyRychVantel; October 13th 2008 at 07:02 AM.
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  4. #4
    Member maybeline9216's Avatar
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    Quote Originally Posted by NyRychVantel View Post


    All the best for your next Wednesday's GCE O Level A.Maths
    Wah how u know i having o lvls?? anyway, thanks
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