Find the equation of the circle through the points \(A(2,0)\), \(B(8,0)\), and \(C(10,4)\), and prove that it touches the \(y\)-axis.

Without the use of tables [or calculators] or measurement, find the equation of the other tangent to this circle from the origin.

Might the resource Finding circles help us here?

How can we decide whether a line is tangent to a circle, or misses it completely, or cuts through it?