Question

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that  EB = EC. 

Answer 1

 EB = EC

 Since, AD and BC are parallel to each other, so,

\[\angle ECB = \angle EDA \left( \text{ Corresponding angles }  \right)\]
\[\angle EBC = \angle EAD \left( \text{ Corresponding angles}  \right)\]
\[\text{ But } , \angle EDA = \angle EAD\]
\[\text{ Therefore } , \angle ECB = \angle EBC\]
\[ \Rightarrow EC = EB\]
\[ \text{ Therefore, }  \bigtriangleup \text{ ECB is an isosceles triangle }  .\]