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In the given figure, AB and CD are two c...

In the given figure, AB and CD are two chords of a circle, intersecting each other at a point E . Prove that
`/_ AEC = (1)/(2) (` angle subtended by arc CXA, at the centre `+` angle subtended by arc DYB at the centre).

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Join AC, BC and BD
Since AC is a chord , we have
`/_ AOC = 2 /_ ABC` ...(i)
Similarly , `/_ DOB = 2/_DCB`. ....(ii)
`:. /_ AOC+ /_ DOB = 2 ( /_ ABC+ /_ DCB ) = 2 /_ AEC`.
Hence, `/_ AEC = (1)/(2) ( /_ AOC + /_ DOB)`
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RS AGGARWAL-CIRCLES -EXERCISE 12B
  1. (i) In Figure (1) , O is the centre of the circle . If / OAB = 40^(@) ...

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  2. In the given figure, O is the centre of the circle and /AOB = 70^(@). ...

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  3. In the given figure, O is the centre of the circle. If /PBC = 25^(@) a...

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  4. In the given figure, O is the centre of the circle . If /ABD = 35^(@) ...

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  5. In the given figure, O is the centre of the circle. If / ACB= 50^(@), ...

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  6. In the given figure, /ABD= 54^(@) and / BCD = 43^(@), calculate (i)...

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  7. In the adjoining figure, DE isa chrod parallel to diameter AC of the c...

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  8. In the adjoining figure, O is the centre of a circle . Chord CD is par...

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  9. In the given figure, AB and CD are straight lines through the centre O...

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  10. In the given figure , O is the centre of a circle, /AOB = 40^(@) and /...

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  11. In the adjoining figure, chords AC and BD of a circle with centre O, i...

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

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  13. In the given figure, O is the centre of the circle and / BCO = 30^(@) ...

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  14. In the given figure, O is the centre of the circle, BD = OD and CD |...

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

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  16. In the figure given below, P andQ are centres of two circles, intersec...

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  17. In the given figure, / BAC = 30^(@) . Show that BC is equal to the rad...

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  18. In the given figure, AB and CD are two chords of a circle, intersectin...

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