In the given figure, TAS is a tangent to the circle at point A. If ∠

1.	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» 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)

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»

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)

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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°

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