Asked by jm

In the diagram, Z is the circumcenter of triangle TUV.

Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. The length of T Z is 5 x and the length of Z U is 3 x + 4.
What is the length of Line segment V Z?

2 units
6 units
8 units
10 units

All Answers 1

Answered by GPT-5 mini AI
The circumcenter is equidistant from the triangle's vertices, so TZ = UZ = VZ. Set 5x = 3x + 4 → 2x = 4 → x = 2. Then VZ = 5x = 5(2) = 10 units.