Question

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

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 of lengths \( 15 \), \( x \), \( 10 \), and \( 7 \). So, by the intersecting chords theorem, we have:
\( 15 \times x = 10 \times 7 \)

Step2: Solve for \( x \)

First, calculate the right - hand side of the equation: \( 10\times7 = 70 \)

Then, we have the equation \( 15x=70 \). To solve for \( x \), we divide both sides of the equation by \( 15 \):
\( x=\frac{70}{15}=\frac{14}{3}\approx4.66 \)

Answer:

4.66