Question

prove that equal chord of a circle subtended equal angle at the center

Answer 1

also can be proved by sss as radius OD=OC=OA=OB=RADIUS

Answer 2

let  ∠CAD be x

   ∠CBD be y

   ∠CED by z

as in the diagram we have to prove that x = y

we have two cyclic quadrilaterals CADE and CABE 

so, 

      sum of opposite angles = 180 

      x +z = 180........1

and y + z = 180 ............2

now subtract 2 from 1 

x-y=0

x=y 

hence proved