Question

In the following figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to

• A. 65°
• B. 60°
• C. 50°
• D. 40°

Answer 1

The correct option is C 50°

Here

∠ABC = 90 (Angle in Semicircle)

In ∆ACB

∠A + ∠B + ∠C = 180°

∠A = 180° – (90° + 50°)

∠A = 40°

Or ∠OAB = 40°

AT is the tangent to the circle and OA is the radius.
So, AT is perpendicular to OA.
Therefore, ∠OAT = ∠CAT = 90°

From the figure, it can be written that,
∠CAT = ∠CAB + ∠BAT
∠BAT = ∠CAT - ∠CAB
Therefore, ∠BAT = 90° – 40° = 50°
Therfore, option c is correct.