Question

if a pair of opposite sides of a cyclic quadrilateral are equal, then prove that the other two sides are parallel

Answer 1

let a circle with centre O , BO and OD are the radius ( given )
to prove - angle ALO = OMD 
const.  draw a LM which is OL prependicular on AB and OM prependicular CD . 
 PROOF - angle ALO = angle OMD =90degree ( by const. ) 
 therefore , by alternate interior angle AB parallel to CD .