Question

In VYX, the centroid is Z. Use the diagram to solve the problems.

7. If XR = 24, find XZ and ZR.
8. If XZ = 44, find XR and ZR.
9. If VZ=14, find VP and ZP.
10. If VP=51, find VZ and ZP.
11. If ZO=10, find YZ and YO.
12. If YO= 18, find YZ and ZO.

Answer 1

The values of the length of lines are:

7) XZ = 12 and ZR = 12

8) XR = 88 and ZR is 44

9) VP is 28 and ZP is 14

10) ZP = 25.6 and VZ = 25.5

11) YZ is 10 and YO is 20

12) YZ is 9 and ZO is 9.

What is circumcenter of a triangle?

Let's denote the vertices of the triangle as X, Y and V the circumcenter as Z and the midpoints of the sides opposite the vertices as R, O and P.

ZX = ZR

ZY = ZO

ZV = ZP

This property signifies that the distance from the circumcenter to any vertex is equal to the distance from the circumcenter to the midpoint of the side opposite that vertex.

7) If XR = 24

XZ = 1/2XR = ZR

XZ = ZR = 1/2*24

XZ = 12 and ZR = 12

8) If XZ = 44

XR = 2*XZ

= 2*44

= 88

ZR = XZ = 44

XR = 88 and ZR is 44

9) If VZ = 14

VP = 2*VZ

VP = 2* 14 = 28

ZP = VZ = 14

VP is 28 and ZP is 14

10) If VP = 51

VZ = 1/2*VP

= 1/2*51

VZ = 25.5

ZP = VZ = 25.5

11) If ZO = 10

YZ = ZO = 10

YO = ZO*2

= 10*2 = 20

YZ is 10 and YO is 20

12) If YO = 18

YZ = ZO = 1/2*YO

= 1/2*18

= 9

YZ is 9 and ZO is 9