Question

1. find the value of x. 13 39

Explanation:

Step1: Apply the tangent - secant segment theorem

If a tangent segment and a secant segment are drawn to a circle from an external point, then \(x^{2}=13\times(13 + 39)\).

Step2: Simplify the right - hand side of the equation

First, calculate \(13+39 = 52\). Then \(13\times52=676\). So the equation becomes \(x^{2}=676\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents a length (a non - negative quantity), \(x=\sqrt{676}\).

Answer:

\(x = 26\)