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Through a fixed point (h,k) secants are ...

Through a fixed point (h,k) secants are drawn to the circle `x^(2)+y^(2)=r^(2)`. Show that the locus of the mid points of the position of the secants intercepted by the circle is `x^(2)+y^(2)=hx+ky`.

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AAKASH SERIES-CIRCLES-ADDITIONAL EXERCISE
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  3. If x+3y=0 is a tangent to the circle with centre at (-1,2) then show t...

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  4. Show that the radius of the circle lying in the first quadrant, passin...

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  6. Two circles, each of radius 5 have a common tangent at (1,1), whose eq...

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  7. Show that the angle between the tangents drawn from (-1,3) to the circ...

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  8. If the circles (x-1)^(2)+(y-3)^(2)=4r^(2) and x^(2)+y^(2)-8x+2y+8=0 in...

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  9. Show that the centre of the circle passing through the points (0,0) an...

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  10. If two distinct chords, drawn from the point (p,q) on the circle x^(2)...

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  11. A circle touches the X-axis and also touches externally the circle wit...

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  12. Let C be the circle with centre (0,0) and radius 3. Show that he equat...

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  13. From the origin chords are drawn to the circle (x-1)^(2)+y^(2)=1. Show...

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  14. Through a fixed point (h,k) secants are drawn to the circle x^(2)+y^(2...

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  15. Show that the area of the triangle formed by the tangents from the poi...

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  16. Tangents are drawn from each point on the line 2x+y=4 to the circle x...

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  17. Show that the equation of the locus of the mid points of the chords of...

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  18. Show tha the tangents drawn from the origin in to the circle x^(2)+y^(...

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  19. Let a circle be given by 2x(x-a)+y(2y-b)=0, ab!=0. Show that the con...

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  20. Two tangents are drawn from a point P to the circle x^(2)+y^(2)+2gx+2...

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