prove that line segment joining midpoints of two equal chords of a circle makes equal angles with the chord
Given that : AB and CD are two equal chords. And, M, N are mid point of chord AB and CD respectively.
To prove :
Construction : Join OM and ON
Since the line segment joining the centre of a circle to the midpoint of a chord is perpendicular to the chord. Therefore,
Since AB and CD are equal chords. So, they are equidistant from the other. (i.e., OM =ON)