Quadrilateral inscribed in circle

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Quadrilateral inscribed in circle

by mariah » Sat Feb 04, 2012 4:16 am
Quadrilateral PXQY is inscribed in a circle. Is angle x equal to angle y?
1). Angle P is not equal to Q.
2). PQ is the diameter of the circle.

Oa B

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by Anurag@Gurome » Sat Feb 04, 2012 4:50 am
mariah wrote:Quadrilateral PXQY is inscribed in a circle. Is angle x equal to angle y?
1). Angle P is not equal to Q.
2). PQ is the diameter of the circle.

Oa B
Opposite angles in any quadrilateral inscribed in a circle add to 180º.

(1) Angle P is not equal to Q does not necessarily imply that angle X is equal to angle Y, it may or may not be equal. We need additional info to find this; NOT sufficient.

(2) PQ is the diameter of the circle again implies that in semicircle PYQ, angle PYQ = 90º and in semicircle PXQ, angle PXQ = 90º; SUFFICIENT.

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The correct answer is B.
Anurag Mairal, Ph.D., MBA
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