Question 119
O is the centre of a circle. AB is a chord of the circle but not its diameter. OC is perpendicular to AB. If OC = CB and radius of the circle be 7 cm, then the length of AB is
Solution
Since, OC is perpendicular to AB
Also, OC = BC
=> In $$\triangle$$ OBC
=> $$OB^2 = OC^2 + BC^2$$
=> $$7^2 = 2BC^2$$
=> $$BC = \frac{7}{\sqrt{2}}$$
$$\therefore$$ AB = 2 * AC = $$2 * \frac{7}{\sqrt{2}}$$
= $$7\sqrt{2}$$ cm
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