AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords are on the same side of the centre and the distance between them is 3 cm, then the diameter of the circle is

OA = OC = radius 

OE and OF are perpendicular to AB and CD .

AE = EB = 5cm

CF = CD = 2cm

Let OE = x

In $$\triangle OAE $$ ,

$$ OA^2 = AE^2 + OE^2$$

$$ OA^2 = 5^2 + x^2$$

In $$\triangle OCF$$,

$$OC^2 = 2^2 +(x + 3)^2$$

$$5^2 + x^2 = 2^2 +(x+3)^2$$

$$ 25 + x^2 = 4 + x^2 + 6x +9$$

x =$$\frac{12}{6} =2 cm $$

 $$ OA^2 = 5^2 + x^2 = 25 + 4 = 29$$

OA = $$\sqrt{29}$$

Diameter = 2$$\sqrt{29}$$

So, the answer would be option b)$$ 2 \sqrt{29} cm $$