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

In the given figure , ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produed to F.If `/_ ABC = 92^(@)` and `/_ FAE = 20^(@)` , find `/_ BCD`.

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The correct Answer is:
`/_ BCD = 108^(@)`
`/_ABC + /_ ADC = 180^(@) implies /_ ADC = 88^(@)`,
`AE || CD implies /_ EAD = /_ADC = 88^(@)`
`implies /_ DAF = /_ EAF + /_ EAD = 20^(@) + 88^(@) = 108^(@)`
`/_ BCD = /_ DAF = 108^(@) [ :' ` ext. `/_ ` of a cyclic quad. ` =` int. opp. `/_ ]`
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RS AGGARWAL-CIRCLES -EXERCISE 12C
  1. In the given figure , POQ is a diameter and PQRS is a cyclic quadrilat...

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  2. In the given figure, O is the centre of the circle and arc subtends an...

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  3. In the given figure , ABCD is a cyclic quadrilateral in which AE is dr...

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  4. In the given figure, BD = DC and / CBD = 30^(@), find / BAC.

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  5. In the given figure, O is the centre of the given circle and measure o...

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  6. In the given figure, , Delta ABC is equilateral . Find (i) / BDC , ...

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  7. In the adjoining figure, ABCD is a cyclic quadrilateral in which / BCD...

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  8. In the given figure, O is the centre of a circle and / BOD = 150^(@) ....

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  9. In the given figure , O is the centre of the circle and / DAB = 50^(@)...

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  10. In the given figure, sides AD and AB of cyclic quadrilateral ABCD are ...

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  11. In the given figure, AB is a diameter of a circle with centre O and DO...

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  12. Two chords AB and CD of a circle intersect each other at P outside the...

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  13. In the given figure, O is the centre of a circle. IF / AOD = 140^(@) a...

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  14. In the given figure, Delta ABC is an isosceles triangle in which AB = ...

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  15. In the given figure, AB and CD are two parallel chrods of a circle. If...

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  16. In the given figure, / BAD = 75^(@), / DCF = x^(@) and / DEF = y^(@) ....

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  17. In the given figure, ABCD is a quadrilateral in which AD= BC and / AD...

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  18. Prove that the perpendicular bisectors of the sides of a cyclic qua...

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  19. Prove that the circle drawn with any side of a rhombus as a diameter, ...

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  20. Prove that the centre of the circle circumscribing the cyclic recta...

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