Circles C₁ and C₂ , of radii r and R respectively, touch each other as shown in figure. The line , which is parallel to the line joining the centres of C₁ and C₂ , is tangent to C ₁ at P and intersects C ₂ at A , B . If R ²=2 r ² , then A O

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Circles C₁ and C₂ , of radii r and R respectively, touch each other as shown in figure. The line , which is parallel to the line joining the centres of C₁ and C₂ , is tangent to C ₁ at P and intersects C ₂ at A , B . If R ²=2 r ² , then A O B

Quantrex Academy · Accepted Answer

Correct answer: B. 45^

C ₁( r , 0) C ₂( R , 0) Eq . of AB y = r Eq. of circle C₂ (x-R)²+y²=R² A ( R - R ²- r ² , r ) using R ²=2 r ² B ( R + R ²- r ² , r ) A ( R - r , r ), B ( R + r , r ) Slope of OA = r R - r = m ₁ Slope of OB = r R + r = m ₂ array l = m ₁- m ₂ 1+ m ₁ ~m ₂ =1 =45^ array

Circles C₁ and C₂ , of radii r and R respectively, touch each other as shown in figure. The line , which is parallel to the line joining the centres of C₁ and C₂ , is tangent to C ₁ at P and intersects C ₂ at A , B . If R ²=2 r ² , then A O B

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