Following are the properties of circle 
Property 1: Equal chords subtend equal angles at the center of a circle
Property 2: If Angles subtended by the chords at the center of circle are equal, then chords are also equal
Property 3: The perpendicular from the center of a circle to a chord bisects the chord.
Property 4: The line drawn from the center of circle to bisect a chord; is perpendicular to the chord
Property 5: Equal chords are equidistant from the center of circle
Property 6: Chords equidistant from the center of circle are equal in length
