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Question
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,
OE2 = OC2 – CE2
= 102 – 62
= 100 – 36
= 64
OE = `sqrt(64)`
= 8 cm
In the right ΔOAF,
OF2 = OA2 – AF2
= 102 – 82
= 100 – 64
= 36
OE = `sqrt(36)`
= 6 cm
Distance between the two chords
= OE + OF
= 8 + 6
= 14 cm
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