Computation looks right to me. But simply memorizing theorems does not promote understanding.

Let's see how we get that theorem. The radius through a point of tangency and the tangent at the same point are perpendicular.

$Let\ r = length\ of\ radius\ of\ given\ circle,$

$u + r = length\ from\ the\ given\ circle's\ center\ to\ a\ given\ point\ outside\ the\ circle,$

$x = length\ of\ the\ line\ that\ is\ tangent\ to\ the\ given\ circle\ and\ runs\ through\ the\ given\ point.$

By the Pythagorean Theorem, we have:

$(u + r)^2 = x^2 + r^2 \implies u^2 + 2ru + r^2 = x^2 + r^2 \implies x^2 = u^2 + 2ru = u(u + 2r) \implies x = \sqrt{u(u + 2r)}.$