A chord of a circle is equal to the radius of the circle. Find the angle substended by the chords at a point on the minor arc and also at a point on the major arc.

Question

Philoid · Accepted Answer

We have,

Radius OA = Chord AB

OA = OB = AB

Then, triangle OAB is an equilateral triangle

Therefore,

∠AOB = 60^o (Angle of an equilateral triangle)

By degree measure theorem,

∠AOB = 2 ∠APB

60^o = 2 ∠APB

∠APB = 30^o

Now,

∠APB + ∠AQB = 180^o (Opposite angle of cyclic quadrilateral)

30^o + ∠AQB = 180^o

∠AQB = 150^o

Therefore,

Angle by chord AB at minor arc = 150^o

And, by major arc = 30^o