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Prove that the line joining the mid-poin...

Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre.

Text Solution

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`/_BOC=/_OAZ=90`
corresponding `/_,OC∥YZ`
`/_COA=/_XBO=90^0`
`(OC∥WX)`
`/_BOC+/_COA=180^0`
`AOB` us a straight line therefore `AB` passes through `O`.
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RD SHARMA-CIRCLE -All Questions
  1. Two concentric circle with centre O have A ,\ B ,\ C ,\ D as the p...

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  2. Two circles whose centres are O and O ' intersect at Pdot Through ...

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

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  4. Two circles of radii 10\ c m\ a n d\ 8\ c m intersect and the leng...

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  5. Two circles of radii 5\ c m\ a n d\ 3c m intersect at two points a...

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  6. In Figure, two circles with centres A\ a n d\ B and of radii 5\ c ...

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  7. In Figure, hat A B~= hat A C and O is the centre of the circle. Prove...

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

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

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  10. In Figure, A B=C B\ a n d\ O is the centre of the circle. Prove that B...

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

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  12. Prove that the line of centres of two interesting circles subtends ...

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  13. The radius of a circle is 8cm and the length of one of its chords i...

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  14. Find the length of a chord which is at a distance of 5 cm from the ...

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  15. Find the length of a chord which is at a distance of 4 cm from the ...

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  16. Two chords AB and CD of lengths 5 cm and 11 cm respectively of a ci...

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  17. Suppose you are given a circle. Give a construction to find its cen...

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  18. Prove that the line joining the mid-point of a chord to the centre ...

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  19. Prove that a diameter of a circle which bisects a chord of the circ...

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

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