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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