Question

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

Explanation:

Step1: Use the intersecting chords theorem

When two chords \(HI\) and \(JK\) intersect at a point \(L\) inside a circle, 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. That is \(HL\times LI=KL\times LJ\). Let \(KL = x\). Then \(HL = 10\), \(LI=18\), \(LJ = 25\) and \(KL=x\).
So, the equation is \(10\times18=x\times25\).

Step2: Solve for \(x\)

From \(10\times18=x\times25\), we have \(180 = 25x\). Then \(x=\frac{180}{25}=7.2\).

Answer:

\(7.2\)