Construct a tangent line from an external point to a circle.
Find a tangent-triangle measure with the Pythagorean theorem
Problem
Find the missing measure in the radius-tangent-center right triangle: radius \(r=5\); center-to-external-point distance \(d=13\); tangent length \(\ell~\) unknown.
The tangent point creates the right angle, so the center-to-external-point segment—not the tangent segment—is the hypotenuse. We’ll assign the sides before writing the Pythagorean equation and then keep the nonnegative root required for a length.
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