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If the diagonals of a cyclic quadrilater...

If the diagonals of a cyclic quadrilateral are equal, then the quadrilateral is:

A

rhombus

B

square

C

rectangle

D

none of these

Text Solution

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The correct Answer is:
C
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Given the following statements : A:If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. B: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. Identify these as contrapositive or converse of each other.

If the diagonals of a quadrilateral bisect each other,then the quadrilateral is a parallelogram.

If the diagonals of a quadrilateral bisect each other; then the quadrilateral is a parallelogram.

Definition of Cyclic quadrilateral

If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as __________.

If the diagonals of a cyclic quadrilateral intersect at the centre of a circle , then the quadrilateral is "_______________" .

If the diagonals of a cyclic quadrilateral are perpendicular to each other, show that the line passing through the point of intersection of diagonals and midpoint of a side is perpendicular to the opposite side.

If the opposite sides of a quadrilateral are equal, prove that the quadrilateral is a parallelogram.

If two opposite sides of a cyclic quadrilateral are equal,then the other two sides are parallel.

ARIHANT SSC-GEOMETRY-INTRODUCTORY EXERCISE - 12.5
  1. In the adjoining figure, O is the centre of circle and diameter AC = 2...

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  2. In the adjoining circle C(O,r)the degree measure of minor arc AB=130^@...

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  3. If the diagonals of a cyclic quadrilateral are equal, then the quadril...

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  4. If the given figure, AB is diameter of the circle, C and D lie on the ...

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  5. In the above figure , O is the centre of the circle, AB and CD are dia...

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  6. The quadrilateral formed by the bisectors of the angles of a parallelo...

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  7. DeltaABC and DeltaDBC have a common base and drawn towards one sides. ...

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  8. In the given figure, angleBAC and angleBDC are the angles of same segm...

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  9. In the given figure, O is the centre of the clrcle. angleABO = 60^(@)....

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  10. In the figure ,find the value of x.

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  11. In the adjoining figure, O is the centre of the circle and D angleOBD ...

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  12. In the given figure, DeltaABC is an equilateral triangle. Find angleBE...

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  13. In the given figure, AB is the diameter of the circle. Find the value ...

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  14. In the given figure, ABCD is a cyclic quadrilateral and diagonals D bi...

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  15. In the given figure, ABCD is a cyclic quadrilateral and AB is diameter...

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  16. In the given figure, angleCOB = 40^(@), AB is the diameter of the circ...

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  17. In the given figure, O is the centre of circle. angleAOC = 120^(@). F...

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  18. In the given figure, O is the centre of the circle and angleAOC = 100^...

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  19. In the given figure, O is the centre of circle, angleAOB =100^(@). Fin...

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  20. In the given figure, AB is the diameter of the circle, angleADC = 120^...

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