Question

In the figure, O is the centre of a circle, AB is a chord, and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to ______

 

Options

• 100°

• 40°

• 50°

• 90°

Answer 1

In the figure, O is the centre of a circle, AB is a chord, and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to 50°.

Explanation:

∠AOB = 100°
∠OAB = ∠OBA (∵ OA and OB are radii)
Now, in ∆AOB,
∠AOB + ∠OAB + ∠OBA = 180°
(Angle sum property of A)
⇒ 100° + x + x = 180° [Let ∠OAB = ∠OBA = x]
⇒ 2x = 180° - 100°
⇒ 2x = 80°
⇒ x = 40°
Also, ∠OAB + ∠BAT = 90°
[∵ OA is radius and TA is tangent at A]
⇒ 40° + ZBAT = 90°
⇒ ∠BAT = 50°