ML Aggarwal Solutions Class 9 Math 15th Chapter Circle Exercise 15.2
ML Aggarwal Understanding ICSE Mathematics Class 9 Solutions Fifteenth Chapter Circle Exercise 15.2. APC Solution Class 9 Exercise 15.2.
Exercise 15.2
(1) If arcs APB and CQD of a circle are congruent, then find the ratio of AB : CD.
Solution:
Given, arc APB = arc CQD
∴ AB = CD [Equal arcs of same circle has equal chord]
Or, AB/CD = 1
∴ AB:CD = 1:1
(2) A and B are points on a circle with centre O. C is a point on the circle such that OC bisects ∠AOB, prove that OC bisect the arc AB.
Solution:
Given, OC bisect ∠AOB
∴ ∠AOC = ∠BOC
∴ arc AC = arc BC
[equals angles from centre subtends equal arcs]
∴ OC bisect – arc ACB.
(3) Prove that the angle subtended at the centre of a circle is bisected by the radius passing through the mid-point of the arc.
Solution:
Given, C is the mid-point of arc AB.
∴ arc AC = arc BC
∴ ∠AOC = ∠BOC [equal arcs subtends equal angles at centre]
∴ OC bisects ∠AOB
∴ Radius OC bisect angle substended by arc AB.
(4) In the adjoining figure, two chords AB and CD of a circle intersect at P. If AB = CD, Prove that arc AD = arc CB.
Solution:
Given, AB = CD.
∴ Arc ADB = arc CBD
[Chords of equal lengths substends equal arc]
Now, arc AD = arc ADB – arc BD
Or, arc AD = arc CDB – arc BD [∵ arc ADB = arc CBD]
Or, arc AD = arc CB (Proved)
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