Question

1. what is the value of x? 12.44 15.75 82.3 10

Explanation:

Step1: Recall the intersecting chords theorem

The intersecting chords theorem states that if two chords intersect in a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. So, if we have two chords with segments \(a, b\) and \(c, d\), then \(a\times b = c\times d\).

In this problem, one chord is divided into segments of length \(14\) and \(36\), and the other chord is divided into segments of length \(x\) and \(32\). Applying the theorem: \(14\times36=x\times32\)

Step2: Solve for \(x\)

First, calculate the left - hand side of the equation: \(14\times36 = 504\)

Then, we have the equation \(504 = 32x\). To solve for \(x\), we divide both sides of the equation by \(32\): \(x=\frac{504}{32}\)

Simplify \(\frac{504}{32}\): \(\frac{504\div8}{32\div8}=\frac{63}{4} = 15.75\)

Answer:

15.75