Let the circles C₁:(x- )^2+(y- )^2=r₁^2 and C₂:(x-8)^2+ (y- 15 2 )^2=r₂^2 touch each other externally at the point (6,6) . If the point (6,6) divides the line segment joining the centres of the circles C₁ and C₂ internally in the ratio 2: 1

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Let the circles C₁:(x- )^2+(y- )^2=r₁^2 and C₂:(x-8)^2+ (y- 15 2 )^2=r₂^2 touch each other externally at the point (6,6) . If the point (6,6) divides the line segment joining the centres of the circles C₁ and C₂ internally in the ratio 2: 1 , then ( + )+4 (r₁^2+r₂^2 ) equals

Quantrex Academy · Accepted Answer

Correct answer: B. 130

aligned & 16+ 3 =6 and 15+ 3 =6 & ( , ) (2,3) aligned Also, C ₁ C ₂= r ₁+ r ₂ aligned & (2-8)^2+ (3- 15 2 )^2 =2 r₂+r₂ & r₂= 5 2 r₁=2 r₂=5 & ( + )+4 (r₁^2+r₂^2 ) & =5+4 ( 25 4 +25 )=130 aligned

Let the circles C₁:(x- )^2+(y- )^2=r₁^2 and C₂:(x-8)^2+ (y- 15 2 )^2=r₂^2 touch each other externally at the point (6,6) . If the point (6,6) divides the line segment joining the centres of the circles C₁ and C₂ internally in the ratio 2: 1 , then ( + )+4 (r₁^2+r₂^2 ) equals

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