Question 55

The radius of a circle is 15 cm and the length of one chord of the circle is 20 cm. What is the distance of the chord from the centre of the circle?

Solution

Given,

Radius of the circle = 15 cm

Length of the chord = 10 cm

From the figure,

$$OA^2+AB^2=OB^2$$

$$=$$> $$OA^2+10^2=15^2$$

$$=$$> $$OA^2+100=225$$

$$=$$> $$OA^2=125$$

$$=$$> $$OA=5\sqrt{5}cm$$

$$\therefore\ $$The distance of the chord from the centre of the circle = OA = $$5 \sqrt 5 cm$$

Hence, the correct answer is Option A

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