JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Three circles of radii \(a, b, c\, ( a < b < c )\) touch each other externally. If they have \(x -\) axis as a common tangent, then
- A \(\frac{1}{{\sqrt a }} = \frac{1}{{\sqrt b }} + \frac{1}{{\sqrt c }}\)
- B \(\frac{1}{{\sqrt b }} = \frac{1}{{\sqrt a }} + \frac{1}{{\sqrt c }}\)
- C \(a, b, c\) are in \(A.P.\)
- D \(\sqrt a ,\sqrt b ,\sqrt c \) are in \(A.P.\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{{\sqrt a }} = \frac{1}{{\sqrt b }} + \frac{1}{{\sqrt c }}\)
Step-by-step Solution
Detailed explanation
Length of direct common tangent for circle \({C_1}\) and \({C_2}\) is \(AB = \sqrt {{{\left( {a + b} \right)}^2} - {{\left( {a - b} \right)}^2}} \) For \({C_3}\) and \({C_2}\) Length of direct common tangent for is…
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