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°
Answer: True. ,