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Consider 3 non-collinear points A(9,3), ...

Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also `H(barx,bary)` are the coordinates of the othocentre of triangle ABC whose area be denoted by `Delta`.
If D,E and F are the middle points BC,CA and AB respectively then the area of the triangle DEF is

A

12

B

6

C

4

D

3

Text Solution

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The correct Answer is:
A, B, C, D
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Knowledge Check

  • Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also H(barx,bary) are the coordinates of the othocentre of triangle ABC whose area be denoted by Delta . The value of a+b+R equals

    A
    3
    B
    12
    C
    13
    D
    none of these

  • Consider 3 non-collinear points A(9,3), B(7,-1), and C(1,-1). Let P(a,b) be the center and R is the radius of circle 'S' passing through points A,B,C. Also H(barx,bary) are the coordinates of the othocentre of triangle ABC whose area be denoted by Delta . The ordered pair (barx,bary) is :

    A
    (9,6)
    B
    (9,-6)
    C
    (9,-5)
    D
    (9,5)

  • If (2, 1, 3), ( 3, 1, 5) ana (1, 2, 4) are the mid points of the sides BC, CA AB of DeltaABC respectively, then the perimeter of the triangle is

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    `2sqrt(6)+sqrt(3)`
    B
    `2(2sqrt(6)+sqrt(3))`
    C
    `2(sqrt(6)+3)`
    D
    `sqrt(6)+sqrt(3)`

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