Two circles touch each other at a point O. AB is a simple common tangent to both the circles touching at point A and point B. If radii of the circles are 9 cm and 4 cm, then find AB.

Correct option is C

Given:
Radius PO = 4cm
Radius QO = 9cm
PQ = 4 + 9 = 13cm
AB is tangent.
Formula Used:
For common tangent AB,
​$$AB = \sqrt{(PQ)^2 – (QO - PO )^2 }$$​​
Solution:

​$$AB = \sqrt{(PQ)^2 – (QO - PO )^2 } \\\ \\AB = \sqrt{(13)^2 – (9- 4 )^2 ) }\\\ \\AB = \sqrt{( 169 – 25)} \\\ \\AB = √ 144 \\ \\AB = 12 cm$$​​