In a circle, two chords, AB and CD, measuring 14 cm and 6 cm, respectively, are parallel to each other on the same side of the centre. If the distance between them is 4 cm, find the length (in cm) of the diameter of the circle.​

Correct option is B

Given:

Length of chord AB = 14 cm

Length of chord CD = 6 cm

The distance between the two parallel chords = 4 cm

Concept Used: 

In a circle , perpendicular drawn from the center of the circle to the chord bisect the chord.

Solution:

Length of pq = 4 cm 

ot  = os (radius) 

In $$\triangle$$ops 

(os)² = (op)² + (ps)² 

(os)² = (op)² + (7)²​

(os)² = (op)² + 49

In $$\triangle$$​oqt 

(ot)² = (op + 4)² + (qt)²​

(ot)² = (op + 4)² + (3)²​

(ot)² = (op + 4)² + 9

we know ot = os 

(op + 4)² + 9 = (op)² + 49 

op² + 16 + 8(op) + 9 = (op)² + 49 

8(op) = 49 - 16 - 9

op = 3 cm 

Now, 

(os)² = (3)² + (7)² 

(os)² = 9 + 49 

os = $$\sqrt{58}$$ 

Hence, diameter = $$2\sqrt{58} \ cm$$​​