Mathematics
In the adjoining figure, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively.
Circles
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Answer
In the figure, chords AB ∥ CD and O is the centre of the circle.
Radius of the circle = 15 cm
Length of AB = 24 cm and CD = 18 cm.
Join OA and OC.
AB = 24 cm and OM ⊥ AB.
∴ AM = MB = = 12 cm (As perpendicular to a chord from the center of the circle bisects it)
In right angle triangle OAM,
⇒ OA2 = OM2 + AM2 (By pythagoras theorem)
⇒ OM2 = OA2 - AM2
⇒ OM2 = 152 - 122
⇒ OM2 = 225 - 144
⇒ OM2 = 81
⇒ OM = = 9 cm.
Similarly ON ⊥ CD
CN = ND = = 9 cm
Similarly In right ∆CNO,
⇒ OC2 = ON2 + CN2 (By pythagoras theorem)
⇒ ON2 = OC2 - CN2
⇒ ON2 = 152 - 92
⇒ ON2 = 225 - 81
⇒ ON2 = 144
⇒ ON = = 12 cm.
MN = OM + ON = 9 + 12 = 21 cm.
Hence, MN = 21 cm.
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