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Square inscribed within a circle

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by pareekbharat86 » Sun Dec 15, 2013 3:44 pm
If the vertices of quadrilateral PQRS lie on the circumference of a circle, is PQRS a square?

(1) Side PS is equal in length to a radius of the circle.

(2) The degree measure of minor arc QR is 60.

OA is D.

Just wanted to confirm 2 properties of a square-
1. Do the diagonals of a square bisect each other at right angles?
2. If a square is inscribed within a circle, does each side of the square subtend an arc of 90 degrees?
Thanks,
Bharat.
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by Stuart@KaplanGMAT » Sun Dec 15, 2013 6:39 pm
pareekbharat86 wrote:If the vertices of quadrilateral PQRS lie on the circumference of a circle, is PQRS a square?

(1) Side PS is equal in length to a radius of the circle.

(2) The degree measure of minor arc QR is 60.

OA is D.

Just wanted to confirm 2 properties of a square-
1. Do the diagonals of a square bisect each other at right angles?
2. If a square is inscribed within a circle, does each side of the square subtend an arc of 90 degrees?
Hi!

1. yes, they do (the diagonals of non-square rectangles also bisect each other, but not at right angles).

2. yes! The 4 angles have to add to 360 and they're equal, so each one is 90 degrees.

And, in case anyone is wondering, each statement is sufficient since each one proves that PQRS is NOT a square.

Stuart
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