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Chords of congruent circles which are eq...

Chords of congruent circles which are equidistant from the corresponding centres, are equal.

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Given: `AB` and `CD` are two equal chords of a circle.
To prove: `/_AOB=/_COD`
Proof: In `/_\AOB` and `/_\COD`,
`AB=CD` (Given)
`AO=CO` (radius)
`OB=OD` (radius)
`:./_\AOB~=/_\COD` (By `SSS` congruency)
`=>/_AOB=/_COD` `(CPCT)`
Hence, proved that equal chords of a circle subtend equal angles at the centre.
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RD SHARMA-CIRCLE -All Questions
  1. Equal chords of a circle subtend equal angles at the centre.

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  2. Chords of congruent circles which are equidistant from the correspon...

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  3. Equal chords of congruent circles subtend equal angles at the centre.

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  4. If the angles subtended by two chords of a circle at the centre are ...

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  5. Of any two chords of a circle show that one which is larger is nearer ...

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  6. If the angles subtended by two chords of congruent circles at the co...

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  7. If two equal chords of a circle in intersect within the circle, prove ...

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  8. Two equal chords A B and C D of a circle with centre O , when produced...

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  9. Two equal chords A B and C D of a circle with centre O , when produced...

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  10. Of any two chords of a circle show that the one which is nearer to the...

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  11. Chords of a circle which are equidistant from the centre are equal.

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  12. Equal chords of congruent circles are equidistant from the correspo...

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  13. The length of two parallel chords of a circle are 6c m and 8c mdot If ...

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  14. Equal chords of a circle are equidistant from the centre.

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  15. Two circle with centres A and B intersect at C and Ddot Prove that /A ...

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  16. Prove that the line joining the mid-points of two parallel chords of a...

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  17. Prove that the right bisector of a chord of a circle, bisects the c...

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  18. Prove that the perpendicular bisector of a chord of a circle always ...

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  19. Prove that the line joining the mid-points of two parallel chords of a...

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  20. Two circles of radil 5c m and 3c m intersect at two points and the dis...

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