Question 6

The angle subtended by the chord of length 10 cm is 120° at the centre. Calculate the distance of the chord (in cm) from the centre.

Solution

Given : $$\angle$$ AOB = 120° and AB = 10 cm

To find : OC = ?

Solution : Perpendicular from the centre to the chord bisects the chord, => AC = CB = $$\frac{10}{2}=5$$ cm

Also, $$\angle$$ AOC = $$\angle$$ COB = $$\frac{120}{2}=60^\circ$$

Thus, in $$\triangle$$ BOC,

=> $$tan(\angle COB)=\frac{BC}{OC}$$

=> $$tan(60^\circ)=\frac{5}{OC}$$

=> $$OC=\frac{5}{\sqrt3}$$ cm

=> Ans - (A)

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