Answer:
Using the Pythagorean Theorem, XZ has a length of 19 inches. Therefore, YZ is not tangent to circle x.
Step-by-step explanation:
If YZ is tangent to circle X, then it will form a right angle with the circle's radius (XY).
If triangle XYZ is a right triangle with its right angle at vertex Y, then according to the Pythagoras Theorem, the square of the hypotenuse XZ will be equal to the sum of the squares of the legs XY and YZ:
[tex]XZ^2=XY^2+YZ^2[/tex]
Given that XY = 11.4 inches and YZ = 15.2 inches, then:
[tex]XZ^2=11.4^2+15.2^2\\\\XZ^2=129.96+231.04\\\\XZ^2=361\\\\XZ=\sqrt{361}\\\\XZ=19[/tex]
According to the given diagram, XY measures 19.6 inches. Therefore, triangle XYZ is not a right triangle, and YZ is not perpendicular to XY. Therefore, YZ is not tangent to circle x.
