In the given figure, TAS is a tangent to the circle at the point A. If ∠OBA = 32°, what is the value of x?

Question

In the given figure, TAS is a tangent to the circle at point A. If ∠OBA = 32°, what is the value of x? 

(a) 64° 

(b) 40° 

(c) 58° 

(d) 50°

Answer 1

Answer : (c) 58º 

OA = OB ⇒ ∠OBA = ∠OAB = 32° (Isosceles ∆ property) 

∠AOB = 180° – (∠OBA + ∠OAB) = 180° – 64° = 116° 

⇒ ∠ACB = \(\frac{1}{2}\) × ∠AOB) = \(\frac{1}{2}\) × 116° = 58° 

Also, ∠BAS = x = ∠ACB = 58°   (Angle in alternate segment are equal)