In the given figure, B and C are the centres of the two circles. AD is the common tangent to the two circles. If the ratio of the radius of both the circles is 3 : 5 and AC = 40, then what is the value of DE ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 4√15
Since the ratio of the radius of both the circles is 3 : 5, let DB = 3x and EC = 5x;
Since triangle ABD and ACE are similar, AB : AC = 3 : 5;
∴ AB : BC = 3 : 2
Since AC = 40, BC = 2/5 × 40 = 16
BC = 3x + 5x = 16
⇒ x = 2
∴ BD = 3x = 6 and EC = 5x = 10.
Triangle AEC is the right angle triangle;
AE2 = AC2 – EC2
AE2 = 1600 – 100 = 1500
AE = 10√15
Since AD : DE = 3 : 2
∴ DE = 2/5 × 10√15 = 4√15