Question

given the circle below with chords ( overline{jk} ) and ( overline{lm} ). find the length of ( overline{ln} ). round to the nearest tenth if necessary.

Explanation:

Step1: Apply the intersecting chords theorem

If two chords \(JK\) and \(LM\) intersect at a point \(N\) inside a circle, then \(JN\times NK=LN\times NM\).
Let \(LN = x\). We know that \(JN = 8\), \(NK=24\), \(NM = 10\).
The equation from the theorem is \(8\times24=x\times10\).

Step2: Solve for \(x\)

First, calculate \(8\times24 = 192\). So the equation becomes \(192 = 10x\).
Then, divide both sides by \(10\): \(x=\frac{192}{10}=19.2\).

Answer:

\(19.2\)