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AB is the chord of a circle with centre O and DOC is a line segment originating from a point D on the circle and intersecting AB produced at C such that BC = OD. If ∠BCD = 20°, then &angAOD is equal to

20°
30°
40°
60°

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62.

Two chords of length a unit and b unit of a circle make angles 60° and 90° at the centre of a circle respectively, then the correct relation is

$straight b space equals space square root of 3 space straight a$
$straight b space equals space space 2 straight a$
$straight b space equals space square root of 2 space straight a$
$straight b space equals space 3 over 2 straight a$

63.
Two circles of same radius intersect each other at P and Q. If the length of the common chord is 30 cm and distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles?

25 cm

50 cm

25 cm

Let PQ be the common chord which is 30 cm given.
∴ PR = PQ/2 = 30/2 = 15 cm

Let OO' be the distance between two centres which is 40 cm given.
∴ OR = OO'/2 = 40/2 = 20 cm.

Now, In ΔOPR,

64.

PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If