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

Mathematics

1 answer:

Minchanka [31]3 years ago

5 0

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 $x=1$

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3 years ago

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