There isn't a universal way to do this, just like there isn't a universal way to solve nonlinear equations in one variable. A good place to start, however, would be to attempt to solve an equation for one of the variables, in terms of the other two. If you substitute that into the other equations, you will then have a system of two equations in two variables. Do this again, and you'll have a single variable equation that you'll hopefully know how to solve.
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You can solve the system of equations with three variables using the substitute method, or using matrix operations.
You cannot solve one equation in three unknowns. You need three independent equations.
You need three independent equations to solve for three unknown variables.
This starts with the collocation circle to go through the three points on the curve. First write the equation of a circle. Then write three equations that force the collocation circle to go through the three points on the curve. Last, solve the equations for a, b, and r.
Id say you would do it the same as you do to , multiply them all out so you can take it away etc juct having to find out one other number.