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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.

A) 35cm

B) 30cm

C) 24cm

D) 14cm

### 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

## Discussion (2)

• Oluwaseun

Am so very greatful you solve my problem

$$r = \frac{d}{2} = \cfrac{26\text{cm}}{2} = 13\text{cm}$$
$$r = 13\text{cm}$$
$$x^2 = 13^2 - 5^2$$ (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