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0
Q:

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?

A) 1 only B) 2 only
C) Both 1 and 2 D) Neither 1 nor 2

Answer:   C) 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

Subject: Volume and Surface Area
Exam Prep: Bank Exams
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