A circle with radius x touches another circle with radius 2x externally. What is the length of a direct common tangent?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. .
For a direct common tangent between two circles with radii r1 and r2 and distance between centers d = √[d2 – (r1 – r2)2]
Here, r1 = x and r2 = 2x
d = r1 + r2 = x + 2x = 3x
Length = √[(3x)2 – (2x – x)2] = √[9x2 – x2] = √[8x2] = 2x√2