Question

ax and ex are secant segments that intersect at point x. what is the length of de? 1 unit 3 units 4 1/2 units 4 2/3 units

Explanation:

Step1: Apply the secant - secant rule

If two secant segments \(AX\) and \(EX\) intersect at a point \(X\) outside the circle, then \(XA\times XB=XE\times XD\). Let \(DE = x\). We know that \(XA=7 + 2=9\), \(XB = 2\), \(XD=3\), and \(XE=3 + x\).
So, the equation is \(9\times2=(3 + x)\times3\).

Step2: Solve the equation

First, simplify the left - hand side of the equation: \(9\times2 = 18\). The equation becomes \(18=(3 + x)\times3\).
Divide both sides by 3: \(\frac{18}{3}=\frac{(3 + x)\times3}{3}\). We get \(6=3 + x\).
Subtract 3 from both sides: \(x=6 - 3\).

Answer:

3 units