Radical axis, radical centre and orthogonality

You will write functions that find the radical axis of two circles, test whether two circles are orthogonal, and find the radical centre of three circles. A circle is given as a triple $(g, f, c)$ for $x^2 + y^2 + 2gx + 2fy + c = 0$.

The idea. The radical axis is $2(g_1 - g_2)x + 2(f_1 - f_2)y + (c_1 - c_2) = 0$. Two circles are orthogonal when $2g_1g_2 + 2f_1f_2 = c_1 + c_2$. The radical centre solves two radical axes together.

Your tasks.

1. Finish radical_axis(s1, s2). Return the three numbers (a, b, c) of the line $ax + by + c = 0$.
2. Finish orthogonal(s1, s2). Return True if the circles cut at right angles. Compare with a small tolerance.
3. Finish radical_centre(s1, s2, s3). Return the point $(x, y)$ where the three radical axes meet, or None if the axes of the first two pairs are parallel.