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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