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?

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