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Chords Equidistant from the Center Are Equal

In the follow...

Question

In the following figure OM=ON and AB=12cm. Find the length of CN.

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Solution

Given, OM = ON.
i.e., chord AB and chord CD are equidistant from the centre O.
Hence, they are equal.
$∴$ AB = CD = 12 cm
$(∵$ Chords that are equidistant from the center are equal)

CN = ND
( $∵$ Perpendicular from centre of the circle to a chord bisects the chord)
$∴ C N =$ 6cm

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