We are told that the point P is the circumcenter of â–³ XYZ. According to the Circumcenter Theorem, the circumcenter of a triangle is equidistant from the vertices of the triangle. This means that PX, PY, and PZ have equal lengths.
Since these segments have equal lengths, we can equate the given expressions for PX and PZ to solve for x.
Finally, we can calculate the lengths of any of the segments by substituting the value of x into either of the given expressions.
PX:& 4( 7)+3 =31
PZ:& 6( 7)-11 =31
Because both of these segments have a length of 31, we know PY does as well.
