Let S₁ and S₂ be two circles drawn inside a unit square ABCD, touching each other externally. Further, the circle S₁ touches the sides AD and DC; and the circle S₂ touches the sides AB and BC. If the area of S₂ is twice the area of S₁ , the

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Let S₁ and S₂ be two circles drawn inside a unit square ABCD, touching each other externally. Further, the circle S₁ touches the sides AD and DC; and the circle S₂ touches the sides AB and BC. If the area of S₂ is twice the area of S₁ , then the radius of S₁ is

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Correct answer: D. 3 2 - 4

Let the unit square ABCD be placed in the coordinate plane such that D is at the origin (0,0) , A is at (0,1) , B is at (1,1) , and C is at (1,0) . Circle S₁ touches AD (the y-axis) and DC (the x-axis). Its center is C₁(r₁, r₁) , where r₁ is its radius. Circle S₂ touches AB ( y=1 ) and BC ( x=1 ). Its center is C₂(1-r₂, 1-r₂) , where r₂ is its radius. The distance between the centers of S₁ and S₂ is given by: C₁C₂ = (1-r₂-r₁)^2 + (1-r₂-r₁)^2 = 2 (1 - r₁ - r₂) Since the circles touch each other externally, the dista

Let S₁ and S₂ be two circles drawn inside a unit square ABCD, touching each other externally. Further, the circle S₁ touches the sides AD and DC; and the circle S₂ touches the sides AB and BC. If the area of S₂ is twice the area of S₁ , then the radius of S₁ is

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