Question

If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the centre of the circle by chord is

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.

Answer 2

Answer:

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