Multiple choice

The radii of $2$ circles are $7$ and $2$. If the distance between their centers is $13$, then the length of their common external tangent, is

  1. $10\sqrt {3}$
  2. $\dfrac {25}{2}$
  3. $12$
  4. $\dfrac {23}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The length of the common external tangent is sqrt(d^2 - (R - r)^2), where d is the distance between centers, R=7, r=2. Length = sqrt(13^2 - (7 - 2)^2) = sqrt(169 - 25) = sqrt(144) = 12.

AI explanation

Using the formula for the length of a common external tangent, L equals the square root of (d squared minus (r1 minus r2) squared). Substituting the given values, L equals the square root of (13 squared minus (7 minus 2) squared). This simplifies to the square root of (169 minus 25), which is the square root of 144, giving a length of 12.

Keep practicing — related questions