Question

Which among the following is always a cyclic quadrilateral?

• A. One of the inner angles of a parallelogram is always greater than 90°
• B. Two pairs of sides of a trapezium are parallel
• C. The diagonals of a rhombus are equal in length
• D. A rectangle is always a cyclic quadrilateral

Answer 1

Answer:

D. A rectangle is always a cyclic quadrilateral

Yes, a rectangle is always a cyclic quadrilateral.

A cyclic quadrilateral is a quadrilateral that can be inscribed in a circle, meaning all its vertices lie on the circumference of a circle.

A rectangle has the following properties:

1. Opposite sides are equal and parallel.

2. All angles are right angles (90 degrees).

For a rectangle, the sum of the opposite angles is always 180° (since each angle is 90°), and the opposite angles are congruent. This is a necessary condition for the rectangle to be inscribed in a circle. Therefore, a rectangle can always be inscribed in a circle, making it a cyclic quadrilateral.

So, the statement "A rectangle is always a cyclic quadrilateral" is true.