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

The length of Line segment VZ is 10 units if Z is the circumcenter of triangle TUV. Point Z is the circumcenter of triangle T U V option (D) 10 units is correct.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

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We have:

In the diagram, Z is the circumcenter of the triangle TUV. Point Z is the circumcenter of triangle T U V.

As we know, The vertices of a triangle are equidistant from the circumcenter.

VZ = UZ = TZ

UZ = 3x + 4

TZ = 5x

3x + 4 =5x

5x - 3x =4

2x = 4

x = 2

TZ = 5x = 5(2) = 10 units

Thus, the length of Line segment VZ is 10 units if Z is the circumcenter of triangle TUV. Point Z is the circumcenter of triangle T U V option (D) 10 units is correct.

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