Question 73

If the length of a chord of a circle at a distance of 12 cm from the centre is 10 cm, then the diameter of the circle is

Solution

given, OC = 12 cm

AC = CB = 5 cm [line drawn through the centre of a circle bisects a chord ]

therefore, radius OA = $$ \sqrt OC^2 + \sqrt AC^2 $$

= $$ \sqrt 12^2 + \sqrt 5^2 $$

= $$ \sqrt 169 = 13 cm $$

diametre = $$ 2 \times 13 = 26 $$

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