Question

The angle subtended by a chord at the centre of a circle is 60 degree, the ratio between the radius and chord

Answer 1

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.