Question

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

Answer 1

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
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