Question

given the circle below with secant (overline{gfe}) and tangent (overline{de}), find the length of (overline{de}). round to the nearest tenth if necessary.

Explanation:

Step1: Apply the tangent - secant theorem

The tangent - secant theorem states that if a tangent \(DE\) and a secant \(EFG\) are drawn to a circle from an external point \(E\), then \(DE^{2}=EF\times EG\). Here, \(EF = 13\) and \(EG=13 + 18=31\).

Step2: Calculate \(DE\)

Substitute the values into the formula \(DE^{2}=13\times31\). So, \(DE^{2}=403\). Then, \(DE=\sqrt{403}\approx20.1\)

Answer:

\(20.1\)