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.
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⏩ [Have a glimpse at the diagram above!]
As per the question,
OA= AB = OB
Therefore,
∆OAB is an equilateral triangle.
=> angle AOB = 60°
=> angle ACB = 1/2 angle AOB
[Angle subtended by an arc at the centre is twice the angle at the remaining circle]
=> angle ACB = 1/2 × 60°
=> angle ACB= 30°
Now,
angle ACB + angle ADB = 180°
[opposite angles of cyclic quadrilaterals are supplementary]
=> angle ADB = 180° - angle ACB
=> angle ADB= 180° - 30° = 150°
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