theorem ; Angle subtended by an arc in the segment are equal.
Given: 'o' is the centre of the circle . AB an arc. angle c and angle d are the angles in the same segment with respect to AB.
R.T.P. : angle c =angle d
Construction: join OA and OB
PROOF: angle AOB =2angle ACB........(1)
angle AOB= 2 angle ADB......(2)
from equation 1,2
2 angle ACB= 2 angleADB
THERFORE angle acb =adb
hence angle C = angle D