Answer
$x x_1 + y y_1 = r^2$.
Explanation
In slope form, the line $y = mx + c$ is tangent to the circle $x^2 + y^2 = r^2$ if and only if $c = \pm r\sqrt{1 + m^2}$.
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What is the equation of the tangent line to the circle $x^2 + y^2 = r^2$ at point $(x_1, y_1)$?
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