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Circles

Short Answer Type

51. Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Find the distance between their centres.

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52. A chord 12 cm long is 8 cm away from the centre of the circle. What is the length of a chord which is 6 cm away from the centre?

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53.

In figure A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

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54. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

∵ OA = OB = AB I Given
∴ ∆OAB is equilateral.
∴ ∠AOB = 60°

∵ OA = OB = AB I Given∴ ∆OAB is equilateral.∴ ∠AOB =

| The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

$equals 1 half cross times 60 degree equals 30 degree$

Now, ∵ ADBC is a cyclic quadrilateral.
∴ ∠ADB + ∠ACB = 180°
| The sum of either pair of opposite angles of a cyclic quadrilateral is 180°
⇒ ∠ADB+ 30°= 180°
⇒ ∠ADB = 180° - 30°
⇒ ∠ADB = 150°.

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