Consider the following statements 1 An isosceles trapezium is always cyclic 2 Any cyclic parallelogr...........

Quantitative Aptitude (CDS) Mensuration 2D

Consider the following statements:

1) An isosceles trapezium is always cyclic.

2) Any cyclic parallelogram is a rectangle.

Which of the above statements is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor

Since it is an isosceles trapezium

So angle C = angle D = x let

A = 180 – D = 180 – x (since AB is parallel to CD)

B = 180-x A+C = 180 –x + x = 180 degrees (Property of cyclic quadrilateral)

ABCD is cyclic parallelogram with AB || CD and AD || BC Considering angles A = C = y (Property of parallelogram) and

B=D = x

Also since it is cyclic

A+C = B+D = 180degrees

So x=y=90degrees And also opposite sides are equal being a parallelogram Thus ABCD is a rectangle

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