In a circle of radius 5√13 cm, a chord is at a distance of 10 cm from the centre of the circle. Find the length (in cm) of the chord.

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Let O be the centre of the circle, and AB be the chord at a distance of 10 cm from O. The radius of the circle is 5√13 cm. Draw a perpendicular from O to AB, meeting AB at point M (the midpoint of AB). Let the length of AB be 2x, so AM = x. In right triangle OMA, OA = radius = 5√13 cm, OM = 10 cm, and AM = x. By Pythagoras theorem: OA^2 = OM^2 + AM^2 ⇒ (5√13)^2 = 10^2 + x^2 ⇒ 325 = 100 + x^2 ⇒ x^2 = 225 ⇒ x = 15. Therefore, length of chord AB = 2x = 2 × 15 = 30 cm.

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