Multiple choice

Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is $4$. Then the ratio of the product of the radii to the sum of the radii of the circles is

  1. $16$
  2. $4$
  3. $8$
  4. $\displaystyle\frac{1}{16}$
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A Correct answer
Explanation

For three circles with radii r1, r2, r3 touching externally, the distance from the point of intersection of tangents to the point of contact is given by sqrt(r1*r2*r3 / (r1+r2+r3)). Given this distance is 4, then 16 = r1*r2*r3 / (r1+r2+r3).

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