Question

Proof of theorem- angles subtended by the same arc in the same segment are equal. Please answer soon, need it urgently, exam tom!!!!

Answer 1

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