Question

Solve for x a. 9 b. 14 c. 13 d. 11

Answer 1

We must remember one of the important properties of the secant lines to a circle.

If from a point outside the circle (Q) there are two secant lines that cross the circle at two points A and B for a secant line and C and D for another secant line, then the product of the segments of these two secant lines are equal to each other

$AQ\times BQ=CQ\times DQ$

Let's see the image given by the exercise with the notation of the property:

Applying the rule, we get,

$\begin{gathered} 7(x+7)=6(15+6) \\ 7x+49=6(21) \\ 7x+49=126 \\ 7x=77 \\ x=\frac{77}{7}=11 \end{gathered}$

In that sense, the correct answer is D. x= 11.