Question

given the circle below with chords \\( \overline { j k } \\) and \\( \overline { l m } \\). find the length of \\( \overline { k n } \\). round to the nearest tenth if necessary.

Explanation:

Step1: Apply the intersecting chords theorem

When two chords \(JK\) and \(LM\) intersect at a point \(N\) inside a circle, the products of the lengths of the segments of the chords are equal. That is \(JN\times NK=LN\times NM\).
Let \(KN = x\). We know \(JN = 30\), \(LN=18\), and \(NM = 28\).
So the equation becomes \(30x=18\times28\).

Step2: Solve the equation for \(x\)

First, calculate \(18\times28 = 504\).
Then, from \(30x = 504\), we can solve for \(x\) by \(x=\frac{504}{30}\).
\(x = 16.8\)

Answer:

\(16.8\)