Multiple choice

The number of points such that the tangents from it to three given circles are equal in length, is

  1. $1$
  2. $2$
  3. $3$
  4. $4$
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A Correct answer
Explanation

The locus of points from which tangents to two circles are equal is the radical axis. For three circles, the intersection of the radical axes of the pairs of circles is the radical center, which is a single point.

AI explanation

The locus of points with equal tangent lengths to two circles is their radical axis, which is a straight line. For three given circles, we can form three such radical axes by taking the circles in pairs. These three lines intersect at exactly one unique point called the radical center, so the number of such points is 1.

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