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Question

Circles C1 and C2 , of radii r and R respectively, touch each other as shown in the figure. The line A, which is parallel to the line joining the centres of C1 and C2 , is tangent to C1 at P and intersects C2 at A,B. If R2=2r2, then AOB equals

A
2212
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B
45
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C
60
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D
6712
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Solution

The correct option is B 45

Equation of ABy=r
Equation of circle C2(xR)2+y2=R2
So,point A(RR2r2,r) Using R2=2r2
point B(R+R2r2,r)
A(Rr,r), B(R+r,r)
Slope of OA=rRr=m1
Slope of OB=rR+r=m2
tanθ=m1m21+m1.m2=1θ=45

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