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If the length of a chord is 56 cm which is at a certain distance from the centre of a circle of radius 53 cm. Find distance between chord from the centre of the circle.

If the length of a chord is 56 cm which is at a certain distance from the centre of a circle of radius 53 cm. Find distance between chord from the centre of the circle. Correct Answer 45

From the given data,

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Let AB = 56 cm be a chord of circle with center O and radius OA and OB are both equal to 53 cms in length. 

Draw OP perpendicular to AB

⇒ AP = AB/2 = 56/2 = 28 cm

From ΔOPA, we know that

⇒ OA2 = AP2 + OP2

⇒ 532 = OP2 + 282

⇒ 2809 - 784 = OP2

⇒ OP2 = 2025 cm

⇒ OP = 45 cm

∴ Distance of the chord from the centre of the circle = OP = 45 cm

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