Question

what is the length of $overline{de}$? 4$\frac{1}{2}$ units 3 units 4$\frac{2}{3}$ units 1 unit segments ax and ex are secant - segments that intersect at point x.

Explanation:

Step1: Apply secant - secant rule

If two secant segments are drawn to a circle from an exterior point, then $(AX)(BX)=(DX)(EX)$. Here, $AX = 7 + 2=9$, $BX = 2$, $DX = 3$, and let $DE=x$, so $EX=3 + x$. Then $9\times2=3\times(3 + x)$.

Step2: Solve the equation

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

Step3: Find the value of $x$

Subtract 3 from both sides of the equation $6 = 3+x$ to get $x=6 - 3=3$.

Answer:

3 units