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a circle which touch two side of square of area 1 and passes through exactly one vertex of square so find the radii of circle...??

a circle which touch two side of square of area 1 and passes through exactly one vertex of square so find the radii of circle...??


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Grade:

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Let circle touches the x-axis & y-axis at P & Q respectively. Then
P(a, 0), Q(0, a)
Equation of circle:
(x-a)^{2}+(y-a)^{2} = a^{2}
It passes through one of its vertex whixh is (1, 1). We have
(1-a)^{2}+(1-a)^{2} = a^{2}
a^{2}-4a+2=0
a = \frac{4\pm \sqrt{8}}{2} = 2 \pm \sqrt{2}
a = 2 -\sqrt{2}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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