Question

Given: Circle k(O) Diameter XY tangent WZ, XY = 10, and WZ = 12 .Find: YZ

Answer 1

Answer:

Side YZ is 8 units long.

Step-by-step explanation:

We can deduct form the graph that segment WO is a radius of the circle and XY is its diameters.

By given, we know that $XY = 10$, which means $WO=\frac{XY}{2}=\frac{10}{2}=5$, by radius definition.

An important characteristic of tangents about circles is that the tangent is always is perpendicular to the radius, that means $\angle OWZ = 90\°$ and $\triangle OWZ$ is a right triangle, that means we can use Pythagorean's Theorem to find the side YZ.

$OZ^{2} =WZ^{2}+OW^{2}$

Where $OZ$ is the hypothenuse and $WZ$ , $OW$ are legs of the triangle.

Replacing all given values, we have

$OZ^{2}=12^{2}+5^{2}\\OZ=\sqrt{144+25}=\sqrt{169}\\ OZ=13$

However, by sum of segments, we have

$OZ=OY+YZ$, where $OY=OW=5$ and $OZ=13$

$13=5+YZ\\YZ=13-5\\YZ=8$

Therefore, side YZ is 8 units long.