Two circles touch each other at point O. AB is a simple common tangent to both the circles touching at point A and point B. If the radii of the circles are 9 cm and 4 cm, then find AB.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 12 cm.
Given that
Two circles touch each other at a point O.
AB is a simple common tangent.
If radii of the circles are r1 = 9 cm and r2 = 4 cm,
Length of the common tangent = √[d2 − (r1 − r2)2]
where d is the center distance, d = 9 + 4 = 13
r1 and r2 are the radius of the circles
Length of the common tangent = √132−(9 − 4)2
Length of the common tangent = √169 - 25 = √144 = 12 cm