Question

1. given the circle below with secant \\( \overline{z x} \\) and tangent \\( \overline{w x} \\), find the length of \\( \overline{w x} \\). round to the nearest tenth if necessary. \\( w x= \\)

Explanation:

Step1: Apply the tangent - secant theorem

The tangent - secant theorem states that if a tangent segment \(WX\) and a secant segment \(ZX\) are drawn to a circle from an external point \(X\), then \(WX^{2}=XY\times XZ\).
Here, \(XY = 15\) and \(XZ=15 + 29=44\).

Step2: Calculate \(WX\)

Substitute the values into the formula: \(WX^{2}=15\times44\).
First, calculate \(15\times44 = 660\).
Then, find \(WX=\sqrt{660}\).
\(\sqrt{660}\approx25.7\)

Answer:

\(25.7\)