Question
Question 194
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: Option A
:
Steps of Construction
Step I Taking O as centre and radius=OC = 3 cm, draw a circle.
Step II Join A to C and draw a perpendicular bisector of AC that cuts the circumference of the circle at B and D.
Step III Join B and D.
Step IV Thus, ABCD is a cyclic quadrilateral.
Justification:
In quadrilateral ABCD,
∠B=∠D=90∘    [angle in a semi-circle]
∠A=∠C=90∘Â
⇒∠B+∠D=180∘
and ∠A+∠C=180∘
⇒opposite angles are supplementaryÂ
Since, opposite angles are supplementary, thus the quadrilateral ABCD is a cyclic quadrilateral.
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:
Steps of Construction
Step I Taking O as centre and radius=OC = 3 cm, draw a circle.
Step II Join A to C and draw a perpendicular bisector of AC that cuts the circumference of the circle at B and D.
Step III Join B and D.
Step IV Thus, ABCD is a cyclic quadrilateral.
Justification:
In quadrilateral ABCD,
∠B=∠D=90∘    [angle in a semi-circle]
∠A=∠C=90∘Â
⇒∠B+∠D=180∘
and ∠A+∠C=180∘
⇒opposite angles are supplementaryÂ
Since, opposite angles are supplementary, thus the quadrilateral ABCD is a cyclic quadrilateral.
Was this answer helpful ?
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