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Most Important Selected Qs for JEE AdvancedMathematicsCircle

The centres of two circles C₁ and C₂ each of unit radius are at a distance of 6 unit from each other. Let P be the mid point of the line segment joining the centres of C₁ and C₂ and C be a circle touching C₁ and C₁ , then the radius of circle C is

Correct answer

8

Step-by-step solution

Let A₁, A₂ and M be centres of circle C₁, C₂ and C respectively the common tangent P to C₁ and C touch C₁ at B₁, C at B₂ and C₂ also at B₂ . From right angle A₁ B₁ P aligned & if A₁ P B₁= , & = A₁ B₁ A₁ P = 1 3 & = 2 2 3 & P B₁=2 2 =P B₂ aligned from MPB ₂ aligned & = PB ₂ MB ₂ = 2 2 r & 1 2 2 = 2 2 r & r =8 aligned

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