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Prove that two different circles cann...

Prove that two different circles cannot intersect each other at more than two points.

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If possible, let two different circles intersect at three distinct points A,B,C. Then, these points are clearly noncollinear . So, a unique circle can be drawn to pass through these points.This is a contradiction.
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RS AGGARWAL-CIRCLES -Exercise 12A
  1. A chord of length 30cm is drawn at a distance of 8 cm from the centre ...

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  2. In a circle of radius 5 cm, AB and CD are two parallel chords of lengt...

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  3. Two parallel chords of lengths 30cm and 16cm are drawn on the opposite...

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  4. In the given figure, CD is the diameter of a circle with centre O and...

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  5. In the given figure, a circle with centre O is given in which a diamet...

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  6. In the adjoining figure,OD is perpendicular to the chord AB of a circl...

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  7. In the given figure, O is the centre of a circle in which chords AB an...

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  8. Theorem :-2 The perpendicular from centre of a circle to the chord bis...

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  9. Prove that two different circles cannot intersect each other at mor...

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  10. Two circles of radii 10 cm and 8 cm intersect each other, and the leng...

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  11. Two equal circles intersect in P and Q. A straight line through P meet...

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  12. If a diameter of a circle bisects each of the two chords of a circl...

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  13. AB is the chord of a circle with centreO. AB is produced to C, such th...

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  14. AB and AC are two chords of a circle of radius r such that AB=2AC. If ...

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  15. In the adjoining figure, O is the centre of a circle. If AB and AC are...

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  16. In the adjoining figure, BC is a diameter of a circle with centre O. I...

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  17. An equilateral triangle of side 9 cm is inscribed in a circle. Find...

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  18. In the adjoining figure, AB and AC are two equal chords of a circle wi...

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  19. In the adjoining figure, OPQR is a square. A circle drawn with centre ...

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  20. Two circles whose centres are O and O ' intersect at Pdot Throug...

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