Multiple choice

Find the number of common tangents, if r1 + r2 = C1C2. (With usual notations, r1 & r2 and C1 & C2 are the radii and centres of the two circles.)

  1. 1

  2. 0

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the sum of radii equals the distance between centers (r1 + r2 = C1C2), the circles touch externally at exactly one point. In this configuration, there are 3 common tangents: 2 direct tangents (one above and one below both circles) and 1 transverse tangent at the point of contact. Option A (1 tangent) would mean complete overlap, while option D (4 tangents) requires the circles to be separate without touching.

Keep practicing — related questions