Question

Use the diagram to solve for segments SW and WQ. Show your work and/or explain how you determined the answer

Answer 1

The intersecting chords theorem states that whenever two chords intersect, the product of their pieces is constant.

So, in this case, we have

$\overline{RW}\cdot\overline{WP}=\overline{SW}\cdot\overline{WQ}$

Plugging your values, we have

$8\cdot 9 = 6x \cdot 12x \iff 72=72x^2 \iff x^2=1$

This equation has solutions $x=\pm 1$, but we can't choose $x=-1$, because it would lead to

$\overline{SW}=-6,\quad\overline{WQ}=-12$

So, the only feasible solutions is $x=1$