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In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords?

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#### Solution

Length of the chord (AB) = 16 cm

∴ AF = `1/2 xx 16`

= 8 cm

Length of the chord (CD) = 12 cm

∴ CE = `1/2 xx 12`

= 6 cm

In the right ΔOCE,

OE^{2} = OC^{2} – CE^{2}

= 10^{2} – 6^{2}

= 100 – 36

= 64

OE = `sqrt(64)`

= 8 cm

In the right ΔOAF,

OF^{2} = OA^{2} – AF^{2}

= 10^{2} – 8^{2}

= 100 – 64

= 36

OE = `sqrt(36)`

= 6 cm

Distance between the two chords

= OE + OF

= 8 + 6

= 14 cm

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