Answer: (B) 130 cm
Proof: If a chord and a line from the centre meet, they must be perpendicular. The line from the centre to the chord also bisects the chord. If the distance from the centre of the circle to the chord is 52 cm and the distance of half of the chord is 39 cm, then you can work out using Pythagoras' Theorem the distance of the radius.
r² = 52² + 39²
r² = 4225
r = 65
Thus, the diameter is 2r = 130 cm