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1.
Distance between two points
$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
2.
Distance in polar coordinates
$d=\sqrt{r_1^2+r_2^2-2r_1r_2\cos\left(\phi_2-\phi_1\right)}$
3.
Line - point distance
The distance from the point $P(x_0,y_0)$ to the line $Ax+By+C=0$ is
$d=\dfrac{|Ax_0 + By_0 + C|}{\sqrt{A^2+B^2}}$