NCERT Mathematics Class 9 Exemplar Ch 10 Circles Part 4

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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°

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

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Answer: True. ,