Question

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

Explanation:

Step1: Apply the intersecting chords theorem

When two chords \(HI\) and \(JK\) intersect at a point \(L\) inside a circle, the following relationship holds: \(HL\times LI=JL\times LK\).
Let \(HL = x\). We know that \(LI = 11\), \(JL=10\), and \(LK = 22\).
Substituting these values into the formula gives us the equation \(x\times11=10\times22\).

Step2: Solve the equation for \(x\)

From \(11x = 10\times22\), first calculate \(10\times22=220\). So the equation becomes \(11x=220\).
Then, divide both sides of the equation by \(11\): \(x=\frac{220}{11}\).
Since \(\frac{220}{11}=20\), we find that \(HL = 20\).

Answer:

\(20\)