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Hello - I'm an experienced software developer but new to Sage. I'm trying to solve a system of equations in various ways using Sage online.

Here's the system of equations

var('x y h k r t d')

eq1 = x^2 + y^2 == d^2

eq2 = y == tan(t) * x

eq3 = (x-h)^2 + (y-k)^2 == r^2

eq4 = -1 * r < h < r

eq5 = -1 * r < k < r

I'm trying to solve this in two ways:

1. I'm trying to solve for h and k for a given r using a set of t and d values. This will obviously be an approximation.

2. I'm trying to get all values of d given h, k, r, and t. I think there should be two values. I was trying to get the equations for d but that might not be possible...

If you could provide any insight into the functions to use to get these results or any sample code, I'd appreciate it.

Thanks, Chris