Question

find the segment length indicated. assume that lines which appear to be tangent are tangent.

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown length be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 12\), \(b=16\), and \(x\) is the hypotenuse. So \(x=\sqrt{12^{2}+16^{2}}\).

Step2: Calculate the squares

\(12^{2}=144\) and \(16^{2}=256\). Then \(12^{2}+16^{2}=144 + 256=400\).

Step3: Find the square root

\(x=\sqrt{400}=20\).

Answer:

\(20\)