NCERT Mathematics Class 9 Exemplar Ch 10 Circles Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Exercise 10.2

Q. 1. Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then .

Answer: True. Because the distances from the centre of two chords are equal.

Q. 2. Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then

Answer: False. The angles will be equal only if

Q. 3. Two congruent circles with centres O and O′ intersect at two points A and B. Then

Answer: True. Because equal chords of congruent circles subtend equal angles at the respective centres.

Q. 4. Through three collinear points a circle can be drawn.

Answer: False. Because a circle through two points cannot pass through a point which is collinear to these two points.

Q. 5. A circle of radius 3 cm can be drawn through two points A, B such that

Answer: True. Because AB will be the diameter.

Q. 6. If AOB is a diameter of a circle and C is a point on the circle, then .

Answer: True. As is right angle,

Q. 7. ABCD is a cyclic quadrilateral such that , and

Answer: False, as

Q. 8. If A, B, C, D are four points such that and , then D is the centre of the circle through A, B and C.

Answer: False, because there can be many points D such that and each such point cannot be the centre of the circle through A, B, C.

Q. 9. If A, B, C and D are four points such that and then A, B, C, D are concyclic.

Answer: True. Angles in the same segment.

Q. 10. In Fig. 10.10, if AOB is a diameter and , then

AOB is a Diameter and ∠ ADC = 120°, then ∠ CAB = 30°

Answer: True. ,