Join AY and let AX = a
Diameter = a + 3
Since AB is the diameter, ∠AYB = 90^{∘}
Since XY is perpendicular to AB, ∠BXY = 90^{∘}
BY = =
Consider triangles ABY and BXY
∠ABY is same as ∠XBY and both the triangles are right angled
Therefore they are similar triangles and sides are proportional!
AB/BY = BY/BX = AY/XY
(a+3)/ = /3
3a + 9 = 34
or a = 25/3
Diameter = 25/3 + 3 = 34/3
Circumference = π*d = 34π/3 cm
Correct Answer: (C). 34π/3 cm