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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?

Correct Answer: Both 1 and 2

Explanation:

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 = 180 degrees


So x=y=90 degrees And also opposite sides are equal being a parallelogram


Thus ABCD is a rectangle


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