Question : Find the number of common tangents, if $r_1+r_2=c_1 c_2$. (With usual notations, $r_1\ \text{and}\ r_2$ and $\mathrm{C}_1 \ \text{and}\ \mathrm{C}_2$ are the radii and centres of the two circles.)
Option 1: 1
Option 2: 0
Option 3: 3
Option 4: 4
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Correct Answer: 3
Solution :
Given, C
1
C
2
= r
1
+ r
2
⇒ The circle touches each other externally.
When the circle touches each other externally then there are only three tangents are possible.
⇒ Two direct common tangents and one transverse tangent.
Hence, the correct answer is 3.
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