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Cyclic Quadrilateral

Is A B C D a ...

Question

Is ABCD a cyclic quadrilateral?
I. Points A, B, C and D lie on a circle.
II. ∠B + ∠D = 180°.

(a) if the given question can be answered by any one of the statements but not the other;
(b) if the given question can be answered by using either statement alone;
(c) if the given question can be answered by using both the statements together but cannot be answered by using either statement;
(d) if the given question cannot be answered by using both the statements together.

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Solution

(b) if the given question can be answered by using either statement alone
We have,
I. If A, B, C and D lie on a circle, then ABCD is a cyclic quadrilateral.
II. ∠A + ∠B + ∠C + ∠D = 360° and ∠B + ∠D = 180°
⇒ ∠A + ∠C = 180°
∴ A, B, C and D lie on a circle.
Thus, each one of I and II gives answer to the given question.
Hence, the correct option is (b).

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