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A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of ...


Question

A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord.

Options

A) 35cm

B) 30cm

C) 24cm

D) 14cm

The correct answer is C.

Explanation:

Diameter (d) = 2 radius (r)
\(r = \frac{d}{2} = \cfrac{26\text{cm}}{2} = 13\text{cm}\)
\(r = 13\text{cm}\)
\(x^2 = 13^2 - 5^2\) (Pythagoras' Theorem)
\(x^2 = 169\)cm\(^2 - 25\)cm\(^2 = 144\)cm\(^2\)
\(x = \sqrt{144\text{cm}^2}\)
\(x = 12\)cm
Length of chord = 2x = 12 \(\times\) 12 cm = 24cm

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Discussion (2)

  • Oluwaseun

    Am so very greatful you solve my problem

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  • Diameter (d) = 2 radius (r)
    \(r = \frac{d}{2} = \cfrac{26\text{cm}}{2} = 13\text{cm}\)
    \(r = 13\text{cm}\)
    \(x^2 = 13^2 - 5^2\) (Pythagoras' Theorem)
    \(x^2 = 169\)cm\(^2 - 25\)cm\(^2 = 144\)cm\(^2\)
    \(x = \sqrt{144\text{cm}^2}\)
    \(x = 12\)cm
    Length of chord = 2x = 12 \(\times\) 12 cm = 24cm