Question

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.

Answer 1

In ΔOAB,

AB = OA = OB = radius

∴ ΔOAB is an equilateral triangle.

Therefore, each interior angle of this triangle will be of 60°.

∴ ∠AOB = 60°

∠ACB = `1/2angleAOB`

∠ACB = `1/2(60^@)`

∠ACB = 30°

In cyclic quadrilateral ACBD,

∠ACB + ∠ADB = 180°    ...(Opposite angle in cyclic quadrilateral)

⇒ ∠ADB = 180° − 30° = 150°

Therefore, the angles subtended by this chord at a point on the major arc and the minor arc are 30° and 150° respectively.