O is the centre of the circle of radius 5 cm AB and CD are two parallel chords, on the
either side of the centre, AB = 6cm and CD = 8cm. Find the distance between the two
chords.
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Answer:
• the distance between two equal chords is nothing but the perpendicular to the chords from the centre.
Consider, ∆ AOB and ∆COD
AB||CD( given)
CO=OB(radii of same circle)
AO=OD(radii of same circle)
Hence. ∆ AOB is congurent to ∆COD
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Let the chord AB = 6 cms
chord CD = 8 cms
Let O be the centre of the circle.
Draw OM and ON perpendicular to AB & CD respectively.
Then,
AM = 3 cms and CN = 4 cms since the perpendicular from the centre to the chord bisects the chord.
Therefore we get OM = 4 cms and ON = 3 cms.
Hence the distance between the chords = MN = OM+ON = 4+3 = 7 cms.
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