Find the value of OM- if CD - AB -6 cm and radius of the circle is 5 cm-A- 4 cmB- 6cmC- 5 cmD- 2-8 cm

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Chords Equidistant from the Center Are Equal

Find the valu...

Question

Find the value of OM, if CD = AB = 6 cm and radius of the circle is 5 cm.

4cm

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6cm

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5cm

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2.8cm

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Solution

The correct option is A 4cm
Given CD = 6 cm and radius of the circle is 5 cm.
$∴$ CN = 3cm
( $∵$ The perpendicular to the centre to a chord bisects the chord)
$Δ O N C$ is a right triangle with CN = 3 cm and OC = 5 cm.
$∴$ ON = 4 cm (By Pythagoras' theorem)
But, ON=OM
( $∵$ perpendiculars drawn from the centre to equal chords are equal)
$∴$ OM=4cm

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