Question 68

A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

Solution

OA = OB (radii of circle)

OA = OB = AB (radii and chord are equal)

$$\therefore$$ $$\triangle$$ AOB is an equilateral triangle.

=> $$\angle$$ AOB = $$\angle$$ OAB = $$\angle$$ OBA = $$60^\circ$$

Also, $$\angle$$ OBD = $$90^\circ$$

=> $$\angle$$ OBA + $$\angle$$ ABD = $$90^\circ$$

=> $$\angle$$ ABD = $$90^\circ-60^\circ=30^\circ$$

=> Ans - (A)

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