AB is the common tangent to both circles as shown in the given figure. What is the distance between the centres of the circles?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 30 cm
Given that
Common tangent AB = 18 cm
The radius of small circle CA = 4 cm
In triangle ACE
CE2 = 42 + 32
CE = 5 cm
Triangle ACE is similar to the triangle BDE
BE/AE = BD/CA
15/3 = BD/4
BD = 20 cm
Now, In triangle BDE,
DE2 = 152 + 202
DE = 25 cm
Hence, The distance between centers CD = CE + ED = 5 + 25 = 30 cm