Question

an equilateral triangle ABC is inscribed in a circle with centre O.Find measures of angle BOC ,COA and AOB

Answer 1

Answer:

ΔABC is equilateral

therefore each angle is 60°

i.e angle ABC=ACB=BAC=60°

chord AB subtents angle AOB at the centre and angle ACB on the circle

Therefore,

angle AOB=2*angle ACB

angle AOB=2*60=120°

chord AC subtents angle AOC at the centre and angle ABC on the circle

Therefore,

angle AOC=2*angle ABC

angle AOC=2*60=120°

chord BC subtents angle BOC at the centre and angle BAC on the circle

Therefore,

angle BOC=2*angle BAC

angle BOC=2*60=120°

Answer 2

Answer:

We have,

ΔABC is an equilateral triangle

Since, each angle is 60

o

.

Now, using property Angle subtend at the centre of circle is double angle at any point on circumference of circle

∠BOC=2∠BAC

∠BOC=2×60

o

∠BOC=120

o