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Let A be one point of intersection of tw...

Let `A` be one point of intersection of two intersecting circles with centres `Oa n dQdot` The tangents at `A` to the two circls meet the circles again at `Ba n dC` , respectively. Let the point `P` be located so that `A O P Q` is a parallelogram. Prove that `P` is the circumcentre of the triangle `A B Cdot`

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A DAS GUPTA-Circles-EXERCISE
  1. A circle of radius r passes through the origin O and cuts the axes at ...

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  2. Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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