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Q.

Two circles in the first quadrant of radii r1 and r2 touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x + y = 2. Then r12+r22−r1r2 is equal to__________.

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answer is 7.

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Detailed Solution

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 Let the circle be (x−r)2+(y−r)2=r2
d=r+r−22=2(r−1)
Now, (2(r−1))2+1=r2
2(r2−2r+1)+1=r2⇒r2−4r+3=0 ⇒r=1,3 ∴       r12+r22−r1r2=9+1−3=7

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