Calculate the length of a chord which is at a distance 12 cm from the centre of a circle of radius 13 cm.

From figure, AB is the chord which is at a distance 12 cm so, OC = 12 cm and OA = radius = 13 cm. In right angle triangle OAC, ⇒ OA 2 = OC 2 + AC 2 (By pythagoras theorem) ⇒ 13 2 = 12 2 + AC 2 ⇒ AC 2 = 13 2 - 12 2 ⇒ AC 2 = 169 - 144 = 25 ⇒ AC = = 5 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ CB = AC = 5 cm. AB = AC + CB = 5 + 5 = 10 cm. Hence, length of chord = 10 cm.

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Mathematics

Calculate the length of a chord which is at a distance 12 cm from the centre of a circle of radius 13 cm.

Circles

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