Multiple choice

lf $(0,\displaystyle \frac{5}{2})$ is a centre of similitude for the circles $\mathrm{x}^{2}+\mathrm{y}^{2}+6\mathrm{x}-2\mathrm{y}+1=0$ and $\mathrm{x}^{2}+\mathrm{y}^{2}-2\mathrm{x}-6\mathrm{y}+ 9=0$ then the length of the common tangent of the circles through it is

  1. $6$
  2. $3$
  3. $2$
  4. $1$
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C Correct answer
Explanation

The center of similitude is given as (0, 2.5). The circles have centers C1(-3, 1) and C2(1, 3) with radii r1=3 and r2=2. The length of the common tangent through the center of similitude can be calculated using the power of the point formula, which is sqrt(S1) or sqrt(S2).

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