The centres of two circles are 84 cm apart. If the radii of these two circles are 38 cm and 26 cm, respectively, then which of the following options gives the length (in cm) of a direct common tangent of these two circles?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. .
We know that,
L = √(d2 - (r1 - r2)2)
here,
L = The length of a direct common tangent, d = distance between the centers of the two circles, r1 = radius of the first circle, and r2 = radius of the second circle
Now,
⇒ L = √(842 - (38 - 26)2)
⇒ L = √(7056 - 122)
⇒ L = √(7056 - 144)
⇒ L = √6912
⇒ L =
Thus,
The length of the direct common tangent is