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Question

In the given figure, O is the centre of a circle. AOC is its diameter, such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT = ?


(a) 40°
(b) 50°
(c) 60°
(d) 65°

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Solution

(b) 50°
ABC=900Angle in a semicircleIn ABC, we have: ACB+CAB+ABC=1800500+CAB+900=1800CAB=1800-1400CAB=400Now, CAT=900(Tangents drawn from an external point are perpendicular to the radius at the point of contact)CAB+BAT=900400+BAT=900BAT=900-400BAT=500

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