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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 = ?
∠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°
∠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°