Mathematics
Prove that the perpendicular bisector of a chord of a circle always passes through the centre.
Circles
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Answer
AB is a chord of a circle with centre O.
Let CD be the perpendicular bisector of AB.
∠ACD = 90° [CD ⊥ AB]
Line joining the center of a circle to the midpoint of a chord is perpendicular to the chord.
∠ACO = 90° [Since C is the midpoint of AB, OC ⊥ AB]
∴ ∠ACD = ∠ACO which is wrong
∴ CD must pass through O.
Hence, the perpendicular bisector of a chord of a circle always passes through the centre.
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