A circle touches the lines x = 0 , y = 0 and x + y = 1. If the centre of the circle lies in first quadrant, show that there are two such circles and find their equations. Specify which of these is inscribed whithin the triangle formed by the given lines.

Answer

`(x-a)^(2) + (y-a)^(2) = a^(2)` where `a = (1)/(2)(2 +- sqrt(2))` and `(x-a)^(2) + (y-a)^(2) = a^(2)` where `a = (1)/(2)(2-sqrt(2))`