Circles — sample questions with answers.

1483 verified circles questions sit in the bank for this chapter alone. Here are 4 of them, worked; a free account gets a full, board-pattern paper across whichever chapters you pick.

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1 mark Assertion–Reason

Assertion (A): The angle in a semicircle is a right angle. Reason (R): A diameter subtends 180° at the centre, and the angle at the circumference is half of that.

(A) Both A and R are true and R is the correct explanation of A.	(B) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.	(D) A is false but R is true.

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2 marks Short answer

An arc of a circle subtends 110° at the centre. (i) What angle does it subtend at a point on the remaining part of the circle? (ii) What is the angle subtended by the same arc at another such point?

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(i) 55° (ii) 55° (angles in the same segment are equal)

3 marks Short answer

Points A, B, C, D lie on a circle with centre O. Arc AB subtends ∠ACB = 55° at C. (i) Find ∠AOB. (ii) Find ∠ADB, where D is another point on the major arc. (iii) If AB were a diameter, what would ∠ACB be?

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(i) 110° (ii) 55° (same segment) (iii) 90°

5 marks Long answer

A, B, C, D, E lie on a circle with centre O. Arc AB subtends ∠ACB = 48° at C. (i) Find the angle arc AB subtends at O. (ii) Find ∠ADB and ∠AEB for D, E on the same arc as C. (iii) State the theorem that makes (ii) work. (iv) If instead AB is a diameter, find ∠ACB. (v) Explain why the reflex angle at O for a minor arc equals 360° minus the non-reflex angle.

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(i) 96°. (ii) ∠ADB = ∠AEB = 48°. (iii) Angles in the same segment of a circle are equal. (iv) 90°. (v) The two angles at O (going the two ways round the arc) together make a full turn, 360°.

This is a slice of one chapter. The full bank covers every chapter of CBSE Class 9 Mathematics, board-pattern, with a fresh answer key every time.

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