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A line through the variable point `A(k+1,2k)` meets the lines `7x+y-16=0,5x-y-8=0,x-5y+8=0` at `B ,C ,D ,` respectively. Prove that `A C ,A B ,A D` are in HP.

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A line through the variable point A(k+1,2k) meets the lines 7x+y-16=0,quad 5x-y-8=0,x-5y+8=0 at B,C,D, respectively.Prove that AC,AB,AD are in HP.

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Knowledge Check

  • A straight line through origin O meets the lines 3y=10-4x and 8x+6y+5=0 at point A and B respectively. Then , O divides the degment AB in the ratio.

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    A
    area of quadrilateral ACBP is 100 sq. units
    B
    radius of smaller circle is `sqrt50`
    C
    area of quadrilateral ACBP is 200 sq. units
    D
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