Question

Equilateral triangle abc is inscribed in a circle of.(see figure) Then,what is the measure of angle Boc

Answer 1

Divide the image in 3 triangle: larger ABC and two smaller COA and AOD
In triangle COA, angle OC =30 and the diameter CE bisects the 60 degree in half. Now oc=ac radius of the circle and this makes COA an issoceles triangle thus angle OCA= angle COA=30 and remaining angle COD=180-60=120

Again angle COA= angle ODA+angle AOD 
angle OAD=120-90=30
Angle AOD=60 
thus using 90-60-30, ad=\sqrt{} 3
and again refering to big 90-60-30 traingle ACB and using root 3 as base to find cd=3
and thus area= 1/2*2 \sqrt{} 3* 3=3 \sqrt{} 3