The length of a common external tangent to two circles of an equal radius of 5 units is equal to the diameter of the circle. Which of the following can be the distance between the centers of the circles in units?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10√2.
We know,
Length of the common tangent = √(d2 - 4r2)
Where, r = radius of the circle and d = distance between the centers of the circle.
According to the question;
⇒ 10 = √(d2 - 4 × 52)
⇒ 100 = d2 - 100
⇒ d2 = 200
⇒ d = 10√2