Question

In the diagram, WZ and XZ are diameters of ⊙T, and WY=XZ=6. If mXY=140°, what is the length of YZ? Determine all that apply.

Answer 1

So since XZ is a diameter of it, then it means its 180 degrees — half the circle

Since xy is 140, so is its arc as it is a central angle

to find the measure of YZ, we do this:
\[ 180-140=YZ \]

now for the length of the arc -- we have that secor of the circle whose angle theta is 40 ; radi is half the diameter, so its \(3\) -- thus we write:
\[ \frac{\cancel{40}}{\cancel{360}}\times 2 \pi \times 3 \]
\[ = \frac{1}{9}\times 2 \pi \times 3 \]
\[ =\frac{2\pi \times 3}{9} \]
\[ =\frac{6\pi }{9} \;\;\;\;\;\;\;\; or \;\;\;\;\;\;\; \frac{2\pi }{3} \]