Question

Question 4 (1 point)Solve for x in the following image.X=5UnitsX

Answer 1

SOLUTION

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other. Two Secants Segments Theorem: If two secants are drawn from a common point outside a circle and the segments are labeled as below, then a(a+b)=c(c+d)

Considering our question;

$\begin{gathered} 5(5+x)=x(x+5) \\ \end{gathered}$

Open the bracket and simplify;

$\begin{gathered} 25+5x=x^2+5x \\ x^2=25 \\ x=\sqrt{25} \\ x=5\text{ units} \end{gathered}$

x = 5 units.