Q6 of 26 Page 79

Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.


We draw a circle with center O and AB, CD are the chords of this circle. Diameter PQ bisects AB and CD at M and N respectively.


We know that the line from the center bisecting the chord is perpendicular to the chord.


Therefore,


∠ OMA = ∠ OMB = 90°


Also, ∠ ONC = ∠ OND = 90°


∠ OMA + ∠ ONC = 90° + 90° = 180°


Hence the two chords, AB and CD are parallel to each other.


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