Question

In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30°, prove that BA:AT = 2:1.

Answer 1

x + x = 60 = 180°

2x + 120°

x = 60°

y + 60 = 180°

y = 120°

∠TPA = 90° - 60 = 30°

30 + y + ∠T = 180°

30 + 120 + ∠T = 180°

150° + ∠T = 180°

∠T = 30°

`(BA)/(AT) = (2r)/r = 2/1`