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

Question

Philoid · Accepted Answer

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 = * AOB

= * 60^o

= 30^o

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