Mathematics
Prove that diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it.
Circles
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Answer
Since, AB || CD and ∠OMA = ∠OMB = 90°
From figure,
∠OMA = ∠OND = 90° (Alternate angles are equal)
∠OMB = ∠ONC = 90° (Alternate angles are equal)
∴ ON ⊥ CD or MN ⊥ CD
We know that,
The perpendicular to a chord from the center of the circle bisects the chord.
∴ NC = ND.
Hence, proved that diameter is perpendicular to other chord and bisects it.
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