A bigger circle centre at O and a smaller circle centre at P touch each other externally such that the length of their common tangent LM is 12 cm. If the radius of the bigger circle is 18 cm, then what will be the radius (in cm) of the smaller circle?

Correct option is C

Given:
Radius of one circle as $$r_1$$​ = 18cm.
Distance of common tangent LM=12cm.
Formula Used:
Direct common tangent if circle touch externally = $$2\sqrt{r_1 r_2 }$$​​
Solution:
​$$12 = 2\sqrt{r_1 r_2}\\6 = \sqrt{18 \times r_2}\\\\36 = 18 \times r_2\\r_2 = 2 \, \text{cm}\\$$​​