Geometry of Circles

Join AB , ∠BAT = ∠BCA = 20° (∠in alt. segment)
∠TAC = 180° - ∠ATB - ∠TCA = 180° - 90° - 20° = 70°(∠ sum of Δ)
∠BAC = ∠TAC - ∠BAT = 70° - 20° = 50°
∠ABC = 180° - ∠BAC - ∠BCA = 180° - 50° - 20° = 110°(∠ sum of Δ)

By sine formula ,
AC / sin∠ABC = BC / sin∠BAC
AC / sin 110° = 6 / sin 50°
AC = 7.360 cm

Let O be the centre of the circle ,
reflex ∠AOC = 2∠ABC = 2 * 110° = 220° (∠at centre twice ∠ at ☉ce)
∠AOC = 360 - 220 = 140°

(AC/2) / r = sin (∠AOC / 2)
(7.360/2) / r = sin (140° / 2)
r = 3.9 cm

Choose (B)