Q. 134.4( 5 Votes )

In the given figure, 0 is the center 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°

Answer :

In ABC


ABC = 90°


[Angle in a semicircle is a right angle]


ACB = 50° [Given]


By angle sum Property of triangle,


ACB + ABC + CAB = 180°


90° + 50° + CAB = 180°


CAB = 40°


Now,


CAT = 90°


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


CAB + BAT = 90°


40° + BAT = 90°


BAT = 50°

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