Question

If segments WY and XZ are diameters of circle T, and WY=XZ=6. If minor arc XY= 140 degrees, what is the length of arc YZ?

Answer 1

hello

to solve this question, we need to draw an illustration

since we are looking for the major arc, we would subtract the minor arc from 360 degrees

major arc YZ =

`\begin{gathered} yz=360-xy \\ yz=360-140=220 \end{gathered}`

now, we know the angke on the major arc is equal to 220 degrees, we can use this information to solve for the length of the arc.

length of an arc

`\begin{gathered} L_{\text{arc}}=(\theta)/(360)*2\pi r \\ \theta=angle \\ r=\text{radius} \\ \pi=3.14 \end{gathered}`

but in this question, we were given the diameter of two segements. we can use that information to solve for the radius

`\begin{gathered} radius=(diameter)/(2) \\ \text{diameter}=wx=xz=6 \\ \text{radius(r)}=(6)/(2)=3 \end{gathered}`

let's insert this and other variables into our equation

`\begin{gathered} L_{\text{arc}}=(\theta)/(360)*2\pi r \\ \text{L}_{\text{arc}}=(220)/(360)*2*3.14*3 \\ L_{\text{arc}}=11.513 \end{gathered}`

from the calculations above, the length of the arc YZ is equal to 11.513