Question

ABCD is a square of side 1 unit. A circle passes through vertices A,B of the square and the remaining two vertices of the square lie out side the circle. The length of the tangent drawn to the circle from vertex D is 2 units. The radius of the circle is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let A = (0, 1), B = (0, 0), C = (1, 0), D = (1, 1)

Equation of required circle = $(x-0)(x-0)+(y-0)(y-1)+\lambda \left|\begin{array}{ccc}x& y& 1\\ 0& 1& 1\\ 0& 0& 1\end{array}\right|$

$=x^2+y^2-y+\lambda x=0$

Given $\sqrt{S_{11}}=2$

$\therefore \lambda =3$

$\therefore$ Radius $=\frac{\sqrt{10}}{2}$