Let circle c2 be inscribed in a square with side l

Question

Let circle c2 be inscribed in a square with side length 1. As shown in figure smaller circle c2 is inscribed in the lower right corner of the square so that c2 is tangent to c2 and the two sides of the square then the area of the c2 is

Vikas TU · Accepted Answer

Dear Student,The square ABCD has circle C1 inscribed in it. LetO1E is the radius of C1. As C1 is inscribed in square ABCD, diameter of C1 = 1.Therefore radius O1E = 1/2.AC is the diagonal of square ABCD. AC = √2. Therefore O1C = √2/2.Now we have e = EC = O1C – O1E = √2/2 – 1/2 = (√2 – 1)/2.From the property of length of tangents, we have FC2 = GC x EC.Let r be the radius of smaller circle C2. Then we have FC = r.GC = EC – EG = e – 2r.Hence we have r2 = (e – 2r)e. Which gives us r = (√2 – 1)e = (√2 – 1)2/2.Area of C2 = πr2 = π(√2 – 1)4/4.Cheers!!Regards,Vikas (B. Tech. 4th yearThapar University)

Analytical Geometry> Let circle c2 be inscribed in a square wi...

Let circle c2 be inscribed in a square with side length 1. As shown in figure smaller circle c2 is inscribed in the lower right corner of the square so that c2 is tangent to c2 and the two sides of the square then the area of the c2 is

Tushar Sharma , 7 Years ago

Vikas TU

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Analytical Geometry> Let circle c2 be inscribed in a square wi...

Let circle c2 be inscribed in a square with side length 1. As shown in figure smaller circle c2 is inscribed in the lower right corner of the square so that c2 is tangent to c2 and the two sides of the square then the area of the c2 is

Tushar Sharma , 7 Years ago

Vikas TU

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