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


In ΔOAB,
AB = OA = OB (radii)
Hence ΔOAB is an equilateral triangle
That is each angle of ΔOAB is 60°
∴ ∠AOB = 60°
∠AOB = 2∠ACB [Angle subtended by an arc of a circle at the centre is double the angle subtended by it on any part of the circle]
Hence ∠ACB = 30°
In cyclic quadrilateral ADBC
∠ADB + ∠ACB = 180° (Sum of opposite angles in cyclic quadrilateral is 180°)
⇒ ∠ADB = 180° − 30° = 150°
Therefore, angle subtended by the chord at a point on the major arc and the minor arc are 30° and 150° respectively.


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