Q.

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

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a

80°

b

50°

c

150°

d

90° 

answer is C.

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Detailed Solution

The chord AB is equal to the radius of circle OA and OB are two radii of circles.
From Δ OAB,  AB = OA = OB = radius of circle.
Δ OAB is an equilateral triangle
AOC = 60°
ACB = 12 × AOB
ACB = 12 × 60° = 30°
ACBD is a cyclic quadrilateral.
ADB + ACB = 180°
ADB = 180° – 30° = 150°.
 
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