Find the points where the circle `x^2+y^2-10x-10y+40=0 ` and the line y+2x=10 intersect.Find the equation of the tangent to the circle at each of the points of intersection.

Explanation

To solve the problem of finding the intersection points of the circle \(x^2 + y^2 - 10x - 10y + 40 = 0\) and the line \(y + 2x = 10\), and then finding the equations of the tangents to the circle at those intersection points, we can follow these steps:

### Step 1: Rewrite the equation of the line
First, we rewrite the equation of the line in terms of \(y\):
\[ y = 10 - 2x \]

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