If AB and CD are two parallel chords of a circle whose centre is O and radius is 20 cm, If AB= 24 cm and CD = 32 cm, find the distance between AB and CD, if it is given that they lie,
i)On opposite sides of the centre O
ii)On the same side of the centre O.
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Solution
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Given
Δ ANO is a right angle triangle,
∴ using pythogoras theorem,
OA
2
=ON
2
+AN
2
13
2
=ON
2
+12
2
ON
2
=13
2
−12
2
=169−144
ON
2
=25
⇒ON
2
=5cm
Similarly for ΔOCM
OC
2
=OM
2
+CM
2
13
2
=OM
2
+5
2
OM
2
=13
2
−5
2
OM
2
=169−25
OM=
144
=12cm
∴ Distance between chorts
=OM+ON
=12+5
=17cm.
Thus the distance between the two chords is 17cm.
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