Question

find x to the nearest tangent. 1.

Explanation:

Step1: Apply the intersecting chords theorem

If two chords intersect in a circle, then \( (a)(b)=(c)(d) \). Here, one chord is divided into segments of lengths \( 5 \) and \( x \), and the other chord is divided into segments of lengths \( 11 \) and \( 11 \). So, \( 5\times x=11\times11 \).

Step2: Solve for \( x \)

From \( 5x = 121 \), we can find \( x=\frac{121}{5}=24.2 \).

Answer:

\( 24.2 \)