Please help me with the process of finding the equation of a circle in the first quadrant that is tangent to the x-axis, y-axis, and a line of the form ax+by+c=0. Thanks.
A circle is tangent to the x-axis iff , is tangent to the y-axis iff , and since the circle's center is in the first quadrant this means that the circle's equation is , and center at
Finally, the distance from a given point to a given line is given by . Do some maths now.
See the attachment...
the triangle contains pairs of identical right-angled triangles,
where c is the length of the hypotenuse, the 3rd side of the triangle.
Then it is straightforward to find r.
Tonio's method finds both solutions.
the circle of r=6 is also tangent to all 3 lines.
The colour of the bisector correspond to the colour of the circle. All three angle bisectors form a right triangle.