Question 1163741
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The centers of both circles are equidistant from both axes; so let the coordinates of the centers of the circles be (h,h).<br>
Using the distance formula to say that the distance from (9,2) to (h,h) is equal to h should give us two values for h, giving us the centers of the two circles.<br>
{{{(h-9)^2+(h-2)^2 = h^2}}}
{{{h^2-18h+81+h^2-4h+4 = h^2}}}<br>
That is indeed a quadratic equation; it will give us two solutions.<br>
I leave it to you to do the work to finish the problem.<br>
Note both values of h are whole numbers; if you're not getting that result, something is wrong with your work....<br>