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Two concentric circle with centre O ha...

Two concentric circle with centre `O` have `A ,\ B ,\ C ,\ D` as the points of intersection with the line `l` as shown in Figure. If `A D=12 c m\ a n d\ B C=8c m ,` find the lengths of `A B ,\ C D ,\ A C\ a n d\ B D`

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Draw `A_|_OM \to\l`
`OM_|_BC \and\ OM_|_AD`
We know that perpendicular lines to a chord which pass through center bisect the chord
`=>BM=MC= 1/2BC=4 cm`
`AM=MD=1/2 AD=6 cm`
`AB=CD=AM–BM=6–4=2cm`
`AC=BD=AB+BC=2+8=10 cm`
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RD SHARMA-CIRCLE -All Questions
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  2. A B\ a n d\ C D are two parallel chords of a circle whose diameter i...

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  3. Two concentric circle with centre O have A ,\ B ,\ C ,\ D as the p...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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