Question 74

A chord of length 8 cm subtends an angle $$60^\circ$$ at the centre. What is the radius of the circle?

Solution

Let O be the center of a circle in which a cord AB = 8 cm long such that angle

AOB = 60°.

In triangle OAB , OA = OB = r. , (radii of same circle)

Thus , angle OAB= angle OBA. = x°(let).

x°+x°+60° = 180°

or. 2x° =120° => x = 120°/2 = 60°

Hence the triangle OAB is an equilateral triangle ,so that

OA = OB = AB = 8 cms. Answer.

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