Question

1 fill in the blank 1 point find the missing value. 2 essay 1 point student reflection: think about the opportunities to share your thinking today. how was your participation in sh

Explanation:

Step1: Use the intersecting chords theorem

If two chords \(AB\) and \(CD\) intersect at a point \(E\) inside a circle, then \(AE\times EB=CE\times ED\).
Here, \(AE = x\), \(EB=2x\), \(CE = 2\), \(ED = 9\).
So, the equation is \(x\times2x=2\times9\).

Step2: Simplify the equation

Simplify \(x\times2x = 2\times9\) to \(2x^{2}=18\).
Divide both sides of the equation by \(2\): \(x^{2}=\frac{18}{2}=9\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents a length, \(x>0\). So \(x = 3\).

Answer:

\(3\)