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CBSE Class 9 Mathematics Question 20 of 20

Circles — Question 12

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Question

Question 12

Prove that a cyclic parallelogram is a rectangle.

Answer

Let ABCD be the cyclic parallelogram.

Prove that a cyclic parallelogram is a rectangle. NCERT Class 9 Mathematics CBSE Solutions.

We know that opposite angles of a parallelogram are equal.

⇒ ∠A = ∠C .......(1)

⇒ ∠B = ∠D .......(2)

We know that the sum of opposite angles of a cyclic quadrilateral is 180°.

⇒ ∠A + ∠C = 180°

⇒ ∠A + ∠A = 180° (From equation (1))

⇒ 2∠A = 180°

⇒ ∠A = 180°2\dfrac{180°}{2}

⇒ ∠A = 90°.

We know that,

If one angle of a parallelogram is 90°, then it is a rectangle.

Thus, quadrilateral ABCD is a rectangle.

Hence, proved that a cyclic parallelogram is a rectangle.