tangents and circle

[12345]

If I'm told that a circle is tangent to the x-axis, y-axis, and another line with a negative slope, whose equation is given to me (I'm not giving it because I just want to make this a general question),
how could I find the center of the circle?

 

[Deleted member 4993]

One way to do it would be:

Define the triangle that circumscribes the circle.

The angular bisectors meet at the center of the required circle.

The radius will be the x-cordinate (= y-cordinate) of the point of intersection (center).

Tell us what are your thoughts and exactly where you are stuck.

 

[Denis]

Since you're given the equation (of hypotenuse, really), then you
know the dimensions of the right triangle circumscribing the circle;
for a right triangle: r = (a + b - c) / 2