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 ∆OAB, 

AB = OA = OB = radius 

∠∆OAB is an equilateral triangle. 

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

∠AOB = 60°

∠ACB=\(\frac{1}{2}\)∠AOB=\(\frac{1}{2}\)(60°)=30°

In cyclic quadrilateral ACBD,

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

∠ADB = 180° − 30° = 150°

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