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Math Help - Vectors #4

  1. #1
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    Vectors #4

    ABC is a triangle as shown in the diagram below. P, Q and R are the midpoints of the sides BC, CA and AB respectively. O is the point of intersection of the perpendicular bisectors of CA and AB.
    Let OA = a, OB = b and OC = c.

    a) Prove that OP is perpendicular to BC.
    This was pretty straightforward.

    b) Hence prove that the perpendicular bisectors of the sides of a triangle are concurrent.
    What is this question asking? I'm new to both proofs and vectors, so these types of questions are a challenge.

    c) Prove that |a| = |b| = |c|.
    As above.

    EDIT: Forgot to add the diagram. Vectors #4-vec.png
    Last edited by Fratricide; April 29th 2014 at 10:48 PM.
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  2. #2
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    Re: Vectors #4

    for (b) they want you to show that the perpendicular bisectors of the sides of a triangle, in this case OR, OQ, OP, all intersect at the same point, in this case O.

    for (c) they want you to show that the lengths of a, b, c are all equal
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  3. #3
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    Re: Vectors #4

    I think I need more help with part (c). How do I show that they're equal?
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