The EY and DW are both equal to 42 and 70, respectively, as they are equidistant from W. ZE is half of DE, which is 53.
To find the lengths EY, DW, and ZE in triangle DEF, where W is the circumcenter, we can use the properties of the perpendicular bisectors and the fact that the circumcenter is equidistant from all vertices of the triangle.
Since YW is given as 42, and YW is a bisector, EY is also 42 because the circumcenter splits the perpendicular bisector into two equal segments.
For DW, we know that FW is given as 70, and since W is the circumcenter, DW must also be 70, making DW equal to 70.
Lastly, ZE can be found like EY and DW. Since WZ bisects side DE, which is given as 106, each segment of the bisector (ZW and ZE) will be half of DE.
Therefore, ZE is 106/2, which is 53.
The probable question may be:
Consider triangle DEF in the figure below. The perpendicular bisectors of its sides are XW, YW, and ZW. They meet at a single point W. Suppose YW = 42, DZ = 62, and FW = 70. Utilizing this information, determine the following:
1. The length of EY, the segment from vertex E to the perpendicular bisector YW.
2. The length of DW, the segment from vertex D to the perpendicular bisector ZW.
3. The length of DE, the segment connecting vertices D and E.