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A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?

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A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?  [#permalink]

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New post 09 Jul 2018, 21:48
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A
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E

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44% (00:36) correct 56% (00:33) wrong based on 36 sessions

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A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?

(1) PQRS is a rhombus.

(2) Diagonals of PQRS are equal.
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Re: A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?  [#permalink]

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New post 09 Jul 2018, 23:56
amanvermagmat wrote:
A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?

(1) PQRS is a rhombus.

(2) Diagonals of PQRS are equal.


Should be A imo.
If quad is inscribed in a circle it means all corners must be on the circle.
(1) says its a rhombus.
For a Rhombus to be a square, all angles must be equal, and the diagonals should be equal. These properties would be met if a rhombus inscribed in a circle and the diagonal would be equal to the diameter of the circle.
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Re: A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?  [#permalink]

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New post 10 Jul 2018, 03:48
amanvermagmat wrote:
A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?

(1) PQRS is a rhombus.

(2) Diagonals of PQRS are equal.



Statement 1 alone is sufficient to state that PQRS is a square.

A rhombus consists of all equal sides and its diagonals are perpendicular bisectors.
Considering, the quadrilateral PQRS is inscribed inside the circle, all the points of PQRS must lie on the circle.

If all points like on the circle and the sides are to be equal then the diagonals of the rhombus are diameters of the circle. And we know that any triangle formed with one of the sides as the diameter will have the angle opposite to the side to be 90.

Hence, all angles are 90 and all sides are equal.


The answer should be A.
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Re: A quadrilateral PQRS is inscribed in a circle. Is PQRS a square? &nbs [#permalink] 10 Jul 2018, 03:48
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