In the figure given below 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.

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#### Solution

Construction: Join OA and OB

As OM ⊥ AB and ON ⊥ CD

∴ AM = MB = 24/2 cm = 12 cm

CN = ND = 18/2 cm = 9 cm

`:. OM = sqrt(OA^2 -AM^2) = sqrt(15^2 - 12^2) = 9 cm`

`ON = sqrt(OC^2 - CN^2) = sqrt(15^2 - 9^2 ) = 12 cm`

∴ MN = OM + ON = 9 + 12 = 21 cm

Concept: Converse: The chords of a circle which are equidistant from the centre are equal.

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