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.
△ACE and △BDE are similar triangles
EAE/BE = 3/15 = 1 : 5 = AC/BD
Similarly AC/BD = 4/BD = 1/5
BD = 20
△ACE and △BDE are right angle triangles.
In △ACE,
CE2 = AC2 + AE2
CE2 = 16 + 9
CE = 5
In △BDE,
DE2 = BE2 + BD2
DE2 = 225 + 400
DE = 25
Distance between the centers = 25 +5 = 30 cm