Q1 of 100 Page 17

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is

Let AB be the chord of length 16cm.

Given that,


Distance from centre to the chord AB is OC = 15 cm


Now,


OC ⊥ AB


Therefore,


AC = CB (Since perpendicular drawn from centre of the circle bisects the chord)


Therefore,


AC = CB = 8 cm


In right ΔOCA,


OA2 = AC2 + OC2


= 82 + 152


= 225 + 64


= 289


OA = 17 cm


Thus, the radius of the circle is 17 cm

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