Question

1. what is the measure of \\( \overline{yz} \\)?

is \\( \overline{xw} \\) tangent to circle z?
select
yes
no

Explanation:

Step1: Recall the Pythagorean theorem

If \(XW\) is tangent to the circle \(Z\) at \(X\), then \(\angle ZXW = 90^{\circ}\) (a tangent to a circle is perpendicular to the radius at the point of tangency). By the Pythagorean theorem \(WZ^{2}=WX^{2}+XZ^{2}\).
We know \(WX = 16\), \(XZ=12\), and \(WZ=WY + YZ=8 + 12=20\) (since \(YZ\) is given as \(12\) in the first - part of the problem).

Step2: Check the Pythagorean theorem

Calculate \(WX^{2}+XZ^{2}\): \(16^{2}+12^{2}=256 + 144=400\).
Calculate \(WZ^{2}\): \(20^{2}=400\).
Since \(WX^{2}+XZ^{2}=WZ^{2}\), \(\angle ZXW = 90^{\circ}\)

Answer:

Yes