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 = ?

Question

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 = ?

Philoid · Accepted 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°