Question

Point Pis the circumcenter of A XYZUse the lengths of PX and

PY to find the length of PZ. Show (or explain) all of your work!
PX - 3x + 2
PY - 4x - 8

Answer 1

The length of the line segment PZ is 32 units.

Explanation:

If P is the circumcenter of
`\triangle XYZ`, then the measures of line segments PX, PY and PZ are the same of the radius of the circle, in which is inscribed in, meaning that measures of the three line segment are equal:

`PX = PY = PZ` (1)

If we know that
`PX = 3\cdot x + 2` and
`PY = 4\cdot x - 8`, then we solve (1) for
`x`:

`3\cdot x + 2 = 4\cdot x - 8`

`x = 10`

Then, the length of PZ is:

`PZ = 3\cdot x + 2`

`PZ = 3\cdot (10) + 2`

`PZ = 32`

The length of the line segment PZ is 32 units.