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

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

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

Answer

Explanation:

Step1: Apply the secant - secant rule

If two secant segments are drawn to a circle from an exterior point, then $AX\times BX=EX\times DX$. Here, $AX = 7 + 2=9$, $BX = 2$, $DX = 3$, and let $DE=x$, so $EX=3 + x$. Then $9\times2=(3 + x)\times3$.

Step2: Solve the equation

First, expand the right - hand side of the equation: $18 = 9+3x$. Then subtract 9 from both sides: $3x=18 - 9=9$. Divide both sides by 3, we get $x = 3$.

Answer:

3 units