If two circles with centres C1 and C2 with radii r1 and r2 is given and also C1C2 = |r1 – r2| is given then –

  1. circles touch each other internally with 1 common tangent
  2. circles touch each other externally with 3 common tangents
  3. circles cut each other  with 2 common tangent
  4. circles neither touch nor cut and  with 4 common tangent

Answer (Detailed Solution Below)

Option 1 : circles touch each other internally with 1 common tangent
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Detailed Solution

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CONCEPT:

  • If C1C2 = |r1 – r2| then given two circles touch each other internally.


Hence, number of common tangents to the given circles in this case = 1.

CALCULATION:

As we know that If C1C2 = |r1 – r2| then given two circles touch each other internally.

Hence, number of common tangents to the given circles in this case = 1.

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