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Mark any three collinear points A, B and C in your notebook, join them to make a triangle and name it.

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Knowledge Check

  • In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC y coordinate of the circumcentre of triangle ABC must be ac

    A
    `(ac)/(a+b+c)`
    B
    `(a^(2)c^(2)-b^(4))/(a^(3)+b^(3)+c^(3))`
    C
    `((b^(2)c^(2)+a^(2)b^(2)-a^(2)c^(2))/(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2)))`
    D
    `(b^(3)(a^(2)+c^(2)))/(2(b^(2)c^(2)+a^(2)c^(2)+a^(2)b^(2)))`
  • If a, b and c are three non-collinear points and ka+2b+3c is a point in the plane of a, b, c then k=

    A
    4
    B
    5
    C
    `-5`
    D
    `-4`
  • In three dimensions there may be more than one point, which are equidistant from three given noncolliner points A,B,C. One of these points will be circumcentre of the triangle ABC The y coordinate of orthocentre of the triangle ABC

    A
    `((3a^(2)c^(2)-a^(2)b^(2)-b^(2)c^(2))/(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2)))`
    B
    `(ab+b^(2)-ac)/(a+b+c)`
    C
    `b-(2(a^(2)c^(2)-b))/(a^(3)+b^(3)+c^(3))`
    D
    `(a^(2)bc^(2))/(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2))`
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