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?

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Cyclic quadrilateral

Rectangle

Rhombus

Square

answer is A.

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Detailed Solution

Drawing a circle using given conditions:
Question Image

In quadrilateral ABCD,

∠ B = ∠ D = 90 ° ∠ A = ∠ C = 90 ° ∴ ∠ B + ∠ D = 180 ° a n d ∠ A + ∠ C = 180 °

Since the opposite angles are supplementary, this quadrilateral is a cyclic quadrilateral.
Hence, option 1 is correct.

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