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In the given figure, L and M are the mid...

In the given figure, L and M are the midpoints of two equal chords AB and CD of a circle C(O,r).
Prove that (i) `/_OLM = /_ OML`
(ii) `/_ALM = /_ CML`.

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Proof Since L is the midpoint of chord AB, we have `OL _|_ AB`.
Again, M is the midpoint of chord CD.
`:. OM _|_ CD`
But, equal chords of a circle are equidistant from the centre.
`:. AB= CD implies OL =OM`
`implies /_ OLM = /_ OML` ...(i)
Now, `/_ ALM = /_ OLA - /_ OLM =90^(@)-/_OLM`
`/_ CML = /_ OMC - /_ OML =90^(@) - /_ OML`.
But `/_ OLM= /_OML ` [ from (i) ],
`:. /_ALM =/_ CML`
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RS AGGARWAL-CIRCLES -MULTIPLE CHOICE QUESTION(MCQ)
  1. In the given figure, L and M are the midpoints of two equal chords AB ...

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  2. In the given figure, BOC is a diameter of a circle and AB =AC . Then ,...

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  3. In the given figure, O is the centre of a circle and / ACB = 30^(@) ...

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  4. In the given figure, O is the centre of a circle. If angle OAB = 40^(@...

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  5. In the given figure, AOB is a diameter of a circle with centre O such...

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  6. AB and CD are two equal to chord of a circle with centre O such that ...

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

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  8. In the given figure, O is the centre of a circle and diameter AB bisec...

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  9. In the given figure, BOC is a diameter of a circle with centre O . If ...

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  10. In the given figure, AB is a chrod of a circle with centre O and AB is...

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  11. In the given figure, AB is a chord of a circle with centre O and BOC i...

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  12. In the given figure, Delta ABC and Delta DBC arre inscribed in a circ...

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  13. In the given figure, BOC is a diameter of a circle with centre O. If /...

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  14. In the given figure, O is the centre of a circle . If / OAC = 50^(@) t...

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  15. In the given figure, O is the centre of a circle in which / OBA = 20^(...

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  16. In the given figure, O is the centre of a circle. If / AOB = 100^(@) a...

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  17. In the given figure, O is the centre of a circle . The, / OAB = ?

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  18. In the given figure, O is the centre of a circle and / AOC = 120^(@) ....

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  19. In the given figure, O is the centre of a circle and / OAB=50^(@). The...

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  20. In the given figure, AB and CD are two intersecting chords of acircle...

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  21. In the given figure, O is the centre of a circle and chords AC and BD ...

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