Question

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

Explanation:

Step1: Use the Chord - Chord Product Theorem

If two chords \(FG\) and \(HI\) intersect at a point \(J\) inside a circle, then \(FJ\times JG=HJ\times JI\). Let \(IJ = x\). We know that \(FJ = 13\), \(JG=3\), and \(HJ = 8\).

Step2: Substitute the values into the formula

Substitute the values into the equation \(FJ\times JG=HJ\times JI\). So, \(13\times3 = 8\times x\).

Step3: Solve for \(x\)

We have the equation \(39=8x\). Then \(x=\frac{39}{8}=4.875\approx4.9\)

Answer:

\(4.9\)