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In the given figure, ABCD is a cyclic qu...

In the given figure, ABCD is a cyclic quadrilateral . A circle passing through A and B, meets AD and BC in E and F respectively. Prove that `EF ||DC`.

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Join EF.
Now, ABFE being a cyclic quadrilateral, we have
`/_ 1+ /_ 2 = 180^(@)` …..(i)
Also, ABCD being a cyclic quadrilateral , we have
`/_ 1 + /_ 3 = 180^(@) ` …....(ii)
From (i) and (ii) , we get
`/_ 1+/_ 2 = /_1 +/_ 3implies /_ 2 = /_ 3`
But, there are corresponding angles
`:. EF || DC`
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RS AGGARWAL-CIRCLES -MULTIPLE CHOICE QUESTION(MCQ)
  1. In the given figure, ABCD is a cyclic quadrilateral . A circle passing...

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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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