Question

1. find the value of the variable. 15 10 7 x 4.66 2.2 10.5 12.0

Explanation:

Step1: Recall the intersecting chords theorem

When two chords intersect in a circle, the products of the lengths of their segments are equal. So, if two chords \( AB \) and \( CD \) intersect at point \( E \), then \( AE\times EB = CE\times ED \).

In this problem, let the two chords be divided into segments: one chord has segments of length \( 15 \) and \( x \), and the other has segments of length \( 10 \) and \( 7 \). By the intersecting chords theorem, we have the equation:
\( 15\times x=10\times 7 \)

Step2: Solve for \( x \)

First, calculate the right - hand side of the equation: \( 10\times7 = 70 \).
Then, to find \( x \), we divide both sides of the equation \( 15x = 70 \) by \( 15 \):
\( x=\frac{70}{15}=\frac{14}{3}\approx4.66 \)

Answer:

\( 4.66 \) (corresponding to the option "4.66")