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 [tex]XY = 10[/tex], which means [tex]WO=\frac{XY}{2}=\frac{10}{2}=5[/tex], by radius definition.
An important characteristic of tangents about circles is that the tangent is always is perpendicular to the radius, that means [tex]\angle OWZ = 90\°\\[/tex] and [tex]\triangle OWZ[/tex] is a right triangle, that means we can use Pythagorean's Theorem to find the side YZ.
[tex]OZ^{2} =WZ^{2}+OW^{2}[/tex]
Where [tex]OZ[/tex] is the hypothenuse and [tex]WZ[/tex] , [tex]OW[/tex] are legs of the triangle.
Replacing all given values, we have
[tex]OZ^{2}=12^{2}+5^{2}\\OZ=\sqrt{144+25}=\sqrt{169}\\ OZ=13[/tex]
However, by sum of segments, we have
[tex]OZ=OY+YZ[/tex], where [tex]OY=OW=5[/tex] and [tex]OZ=13[/tex]
[tex]13=5+YZ\\YZ=13-5\\YZ=8[/tex]
Therefore, side YZ is 8 units long.
