Multiple choice

There are two circles with centres $c_1\;&\;c_2$ with having radii $3\;cm$. Distance between their centres is $8\;cm$ How many common tangents can be drawn?

  1. $2$
  2. $3$
  3. $4$
  4. $0$
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C Correct answer
Explanation

The sum of the radii of the two circles is 3 cm + 3 cm = 6 cm. Since the distance between their centers is 8 cm, which is greater than the sum of their radii, the two circles lie completely outside each other without intersecting. For two such disjoint circles, there are exactly 4 common tangents: 2 direct and 2 transverse.

AI explanation

To find the number of common tangents, we check the relative positions of the circles using the distance between centers and the sum of their radii. The distance between centers is 8 cm, and the sum of the radii is 3 cm plus 3 cm, which is 6 cm. Because the distance between centers (8 cm) is strictly greater than the sum of the radii (6 cm), the circles lie completely outside each other, resulting in exactly 4 common tangents.

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