Question

The line joining mid-points of two chords of a circle passes through the centre. Prove that the chords are parallel

Answer 1

when the line divides both the chords into 2 equal halves then it means that it is perpendicular to both the chords (theorm of circle states that if a line segment bisects a chord than it is also perpendicular to it)

so by alternate int. angles property ( as both will be 90°) the 2 lines will be paralell

Answer 2

for any chord, a  line passing through midpoint and center is perpendicular bisector from center to the chord
 (proof by congruency of 2 sides and equal angles)

so the if the same line passes through both the midpoints  thethe line is perpendicular bisector for both the lines
so 90° at both ends

 hence parallel