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  4. A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertex, the radius of the circle can be

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Q. $A B C D$ is a square of unit area. A circle is tangent to two sides of $A B C D$ and passes through exactly one of its vertex, the radius of the circle can be

Conic Sections

Solution:

l. $(r-1)^2+(r-1)^2=r^2$
$\Rightarrow r^2-4 r+2=0$
$\Rightarrow r=\frac{4+\sqrt{16-8}}{2}=\frac{4 \pm 2 \sqrt{2}}{2}=2 \pm \sqrt{2}$
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