MATHEMATICS · Multi-part · AoPS · Mathematics · Follow the Rules · One-Variable Linear Equations
Problem
In cyclic quadrilateral ABCD, it is given that ∠ABC=∠ADC.
(i) Prove that chords AD and BC subtend equal angles at every point of the circumference on the same segment.
(ii) Deduce that AD=BC.
(iii) If the common angle measure in part (i) is 65∘, determine ∠BAD and ∠BCD and justify your answer.