Hi there. This is my first post here so plz excuse any mistakes i may make. I was going thur my textbook, and looking at various problems, and before I began my hw a certain problem caught my eye.(adsbygoogle = window.adsbygoogle || []).push({});

In the figure below the circle is tangent to the x-axis, to the y-axis, and to the line 3x+4=12

a) Find the equation of the circle. Suggestion: decide the what the relationships must be between h, k, and r in the equation of a circle. Then find a way to apply it to the following formula: d = (|y0 -mx0-b|)/(sqrt(1+m^2))

b) Let S, T, and U denote the points where the circle touches the x & y axis & line 3x+4y=12. Find the equations through A and T; through B and U; through S and C

c) Where do the line segments AT and CS intersect? Where do AT and BU intersect.

Here is what i have done.

point C is (0,3)

point B is (4,0)

point A is (0,0)

Where i get stuck is at part a. From my POV there is a lack of information making it impossible to continue, but that can't be the case.

I know that the equation of a circle is r^2=(x-h)^2+(y-k)^2 but how am stuck on how to find the solutions for the variables. I know that the point of origin for the circle isn't (0,0), but im not rly given anything else to work with. Everything I have been asked of to do in this problem I can do, BUT only with a little bit more information. If I had the point of origin for the circle I wouldn't have a problem. I haven't even started my HW cuz of this problem. ITs bugging me soo much!!!!!!

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# Homework Help: Gergonne Point of Triangle ABC

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