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Prove that the locus of a point which mo...

Prove that the locus of a point which moves such that the sum of the square of its distances from the vertices of a triangle is constant is a circle having centre at the centroid of the triangle.

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A DAS GUPTA-Circles-EXERCISE
  1. Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2...

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  2. Let A be one point of intersection of two intersecting circles with ce...

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  3. Prove that the locus of a point which moves such that the sum of th...

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  4. The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes i...

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  5. A triangle has two of its sides along the axes, its third side touches...

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  6. The locus of the perpendiculars drawn from the point (a, 0) on tange...

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  7. Let S-=x^2+y^2+2gx+2f y+c= be a given circle. Find the locus of the fo...

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  8. Show that the locus of points from which the tangents drawn to a circl...

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  9. Find the locus of the point of intersection of tangents to the circle ...

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  10. The circle x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two ...

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  11. The locus of the centres of the circles which touch x^2+y^2=a^2 and x^...

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  12. Locus of the point of intersection of perpendicular tangents to the ...

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  13. If the polar of a point (p,q) with respect to the circle x^2 +y^2=a^2 ...

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  14. Find the locus of the centres of the circle which cut the circles x^2+...

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  15. The circle (x-a)^2+(y-a)^2=a^2 is rolled on the y-a xi s in the positi...

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  16. The circle x^2+y^2 - 4x-8y + 16 = 0 rolls up the tangent to it at (2+s...

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  17. The centre of a circle (1, 1) and its radius is 5 units. If the centre...

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  18. The point of intersection of the lines x - y + 1 =0 and x + y + 5 = 0 ...

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  19. A circle touches x-axis at (2, 0) and has an intercept of 4 units on y...

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  20. Tht line L passes through the points f intersection of the circles x ^...

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