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If the quadrilateral formed by the lines...

If the quadrilateral formed by the lines `a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0` has perpendicular diagonals, then `b^2+c^2=b^('2)+c^('2)` `c^2+a^2=c^('2)+a^('2)` `a^2+b^2=a^('2)+b^('2)` (d) none of these

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The correct Answer is:
we have `|{:(a-a',b-b',c-c'),(A,B,C),(A',B',C'):}|=0`
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ARIHANT MATHS-CIRCLE -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(pri...

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  2. A circle is given by x^2 + (y-1) ^2 = 1, another circle C touches it e...

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  3. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

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  4. A circle touches the x-axis and also touches the circle with center (...

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  5. If a circle passes through the point (a, b) and cuts the circlex x^2+y...

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  6. Let ABCD be a square of side length 2 units. C2 is the circle through ...

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  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  8. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  9. If the lines 3x-4y-7 = 0 and 2x-3y-5=0 are two diameters of a circle o...

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  10. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

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  11. Tangents are drawn from the point (17, 7) to the circle x^2+y^2=169, S...

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  12. Consider a family of circles which are passing through the point (-...

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  13. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  14. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  15. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  16. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

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  17. The point diametrically opposite to the point P(1, 0) on the circle x^...

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