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If the distances from the origin of the centers of three circles `x^2+y^2+2lambdax-c^2=0,(i=1,2,3),` are in GP, then prove that the lengths of the tangents drawn to them from any point on the circle `x^2+y^2=c^2` are in GP.

A

A.P.

B

G.P.

C

H.P.

D

none of these

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The correct Answer is:
B
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If the distances from the origin of the centers of three circles x^(2)+y^(2)+2 lambda x-c^(2)=0,(i=1,2,3), are in GP,then prove that the lengths of the tangents drawn to them from any point on the circle x^(2)+y^(2)=c^(2) are in GP.

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MCGROW HILL PUBLICATION-CIRCLES AND SYSTEMS OF CIRCLES -EXERCISE (LEVEL 1 ( SINGLE CORRECT ANSWER TYPE QUESTIONS ))
  1. From the point A (0, 3) on the circle x^2+4x+(y-3)^2=0 a chord AB is d...

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  2. If the lines 3x-4y+4=0a d n6x-8y-7=0 are tangents to a circle, then fi...

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  3. If the distances from the origin of the centers of three circles x^2+y...

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  4. The distance between the chords of contact of tangents to the circle x...

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  5. A variable circle passes through the point A(a ,b) and touches the x-a...

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  6. The locus of a point, which moves such that the lengths of the tangent...

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  7. The circle that can be drawn to touch the coordinate axes and the line...

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  8. Area of an equilateral triangle inscribed in a circle of radius a is

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  9. A point P moves such that PA/PB = p where A and B are two fixed pints ...

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  10. The lengths of the tangents from the points A and B to a circle are l...

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  11. Two circles which pass through the points A(0, a), B (0,-a) and touch ...

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  12. No portion of the circle x ^(2) + y^(2) - 16x + 18y + 1=0 lies in the

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  13. The geometrical mean between the smallest and greatest distance of the...

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  14. The length of the longest ray drawn from the point (4,3) to the circle...

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  15. If y pm a =0 is a pair of tangents to the circle x ^(2) + y ^(2) =a ^...

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  16. The circle x ^(2) + y ^(2) =9 is contained in the circle x ^(2) + y ^(...

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  17. The line (x-1) cos theta + (y-1) sin theta =1, for all values of theta...

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  18. Equation of the circle which cuts each of the circles x ^(2) + y ^(2) ...

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  19. The point at which the circle x ^(2) + y ^(2) + 2x + 6y + 4=0 and x ^(...

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  20. Find the equation of a circle which passes through the point (2,0) ...

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