# 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...??

Jitender Singh IIT Delhi
8 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