Question

1 multiple choice 1 point in the circle shown, chords ac and bd intersect at e. if ae = 8, ec = 6, and be = 4. how long is \\( \overline { d e } \\)?

Explanation:

Step1: Apply the intersecting chords theorem

When two chords \(AC\) and \(BD\) intersect at a point \(E\) inside a circle, the following relationship holds: \(AE\times EC=BE\times DE\).

Step2: Substitute the given values

We know that \(AE = 8\), \(EC = 6\), and \(BE = 4\). Substituting these values into the formula \(AE\times EC=BE\times DE\), we get \(8\times6 = 4\times DE\).

Step3: Solve for \(DE\)

First, calculate \(8\times6=48\). So the equation becomes \(48 = 4\times DE\). Then, to find \(DE\), we use the formula \(DE=\frac{48}{4}\).

Answer:

\(12\)