Question 1077712
The perpendicular bisector of the line segment between the given points will contain the centers of the two circles. That bisector line is:

{{{y = 5 -x}}}

The distance from a point on the line ({{{x}}}, {{{5-x}}}) to one of the points will equal the distance from the point on the line to the y-axis.

{{{(x-1)^2 + ((5-x)-3)^2 = x^2}}}

{{{x^2 -2x + 1 + 25 - 10x + x^2 - 6(5- x) + 9 = x^2 }}}…... expand the left side

{{{x^2 -6x + 5 = 0 }}}...… express in standard form

{{{(x-5)(x-1) = 0}}} … factor

{{{x}}} = { {{{1}}}, {{{5}}} } = { {{{a}}},{{{ b}}} }........ … these are the x-coordinates of the circle centers, and also their radii

{{{a*b = 1*5 = 5 }}}

here is image:

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