Position, chord and tangent length

You will write functions that say where a point is against a circle, find the length of a chord cut by a line, and find the length of a tangent. The checker uses the circles of the lessons.

The idea. For the circle with centre $(h, k)$ and radius $r$, the number $S_1 = (x_1 - h)^2 + (y_1 - k)^2 - r^2$ is negative inside, zero on the circle and positive outside. The distance of the centre from a line $ax + by + c = 0$ is $|ah + bk + c| / \sqrt{a^2 + b^2}$. The chord is $2\sqrt{r^2 - d^2}$, and the tangent is $\sqrt{S_1}$.

Your tasks.

1. Finish power(px, py, h, k, r) to return $S_1$.
2. Finish chord_length(a, b, c, h, k, r) to return the length of the chord that the line cuts, or 0 if the line does not cut the circle.
3. Finish tangent_length(px, py, h, k, r) to return the length of the tangent from the point, or None if the point is not outside.