Question

Draw a circle of radius 3 cm and draw its diameter and label it as AC. Construct its perpendicular bisector and let it intersect the circle at B and D. What type of quadrilateral is ABCD? Justify your answer.

Answer 1

Steps of construction:

Step I: Taking centre OC = 3 cm, draw a circle.

Step II: Join A to C and draw a perpendicular bisector of AC that cuts the circumference of circle at B and D.

Step III: Join B and D.

Step IV: Thus, ABCD is a cyclic, quadrilateral.

Justification: In cyclic quadrilateral,

∠B = ∠D = 90°

∠A = ∠C = 90°   ...[Angle in a semi-circle]

∠B + ∠D = 180°

And ∠A + ∠C = 180°  ...[Opposite angles are supplementary]

Since, opposite angles are supplementary,

Thus, quadrilateral is a cyclic quadrilateral.