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Prove that all the chords of a circle th...

Prove that all the chords of a circle through a given point within it, the least is one which is bisected at that point.

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RD SHARMA ENGLISH-CIRCLE -All Questions
  1. In Figure, equal chords A B and C D of a circle with centre O , cut...

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  2. Two equal circles intersect in P and Q . A straight line through P mee...

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  3. Prove that all the chords of a circle through a given point within it,...

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  4. Prove that the diameter is the greatest chord in a circle.

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  5. Bisector A D of /B A C of /\ A B C passes through the centre O of the ...

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  6. If two sides of a cyclic quadrilateral are parallel, prove that the ...

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  7. The quadrilateral formed by angle bisectors of a cyclic quadrilateral ...

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  8. If two non-parallel sides of a trapezium are equal, it is cyclic. OR A...

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  9. If two opposite sides of a cyclic quadrilateral are equal, then the ...

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  10. The sum of either pair of opposite angles of a cyclic quadrilateral is...

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  11. If the chord of a circle is equal to the radius of the circle, then th...

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  12. If one side of a cyclic quadrilateral is produced, then the exterior ...

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  13. If the sum of any pair of opposite angles of a quadrilateral is 180^@;...

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  14. The sum of the angles in the four segments exterior to a cyclic qua...

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  15. If the bisectors of the opposite angles /Aa n d/B of a cyclic quadrila...

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  16. If O is the circumcentre of a A B C and O D|B C , prove that /B O ...

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  17. Two diameters of a circle intersect each other at right angles. Prove ...

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  18. A B C and A D C are two right triangles with common hypotenuse A Cdot ...

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  19. In a circle with centre O , chords A Ba n dC D intersect inside the ci...

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  20. A B C and A D C are two right triangles with common hypotenuse A Cdot ...

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