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In the given figure, ABCD is a parallelo...

In the given figure, ABCD is a parallelogram. The circle through A,B,C intersects CD produced at E. Prove that AD `=` AE

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It is given that ABCE is a cyclic quadrilateral.
`:. /_ ABC + /_ AED = 180^(@)` .....(i)
Also, EDC is a straight line.
`:. /_ ADE + /_ ADC = 180^(@)`
But,`/_ ADC = /_ABC ` [ opposite `/_ s ` of a `||` gm ]
`:. /_ ADE + /_ABC =180^(@)` ...(ii)
Thus,`/_ ABC + /_ AED = /_ ADE + /_ ABC` [ from (i) and (ii) ]
`implies //_AED = /_ADE`
`implies AD =AE ` [ opposite sides of equal of `/_ s` of `Delta ` ADE ]
Hence, `AD = AE`.
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RS AGGARWAL-CIRCLES -MULTIPLE CHOICE QUESTION(MCQ)
  1. In the given figure, ABCD is a parallelogram. The circle through A,B,C...

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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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