In the given circle, diameter AB is extended to meet chord CD extended at P. If the lengths of the line segments AP, CD and DP are 18 cm, 3 cm and 9 cm, respectively, what is the length of the radius of the circle?

Correct option is A

Given:​

AP = 18 cm,    CD = 3 cm     DP = 9 cm​

Concept Used:

If two secants PA and PC intersect the circle at points B and D, then

AP × BP = CP × DP

​Solution:

AP $$\times$$ BP = CP $$\times$$ DP

18 $$\times$$ x = (3 +9) $$\times$$ 9

18x = 9 $$\times$$12

BP = x = 6 cm

Now,     AB = 18cm - 6cm = 12cm

So, Radius = $$\frac{12}{2}$$ = 6 cm​