Question

In Fig. AT is a tangent to the circle. If m∠ABC = 50°, AC = BC, Find ∠BAT.

Answer 1

AC = BC
⇒ ∠CBA = ∠CAB
⇒ ∠CAB = 50°
∴ ∠ACB = 180° - (50° + 50°) = 80°
Now, ∠BAT = ∠BCA      ....(Angles are in alternate segments)
⇒ ∠BAT = 80°.