The problem provided includes two triangles with known data and asks for the measures of several segments, assuming that the given points $H$ and $T$ are the circumcenters of triangles $\triangle BCD$ and $\triangle MNP$, respectively. To solve for the measures of the segments, we need to use the fact that the circumcenter of a triangle is equidistant from all three vertices of the triangle.

Let's start with the first triangle, $\triangle BCD$:

1. $H$ is the circumcenter of $\triangle BCD$

• Since $H$ is equidistant from $B$, $C$, and $D$, the distances from $H$ to each of the vertices are the same.
• From the given lengths:
  • $HE = 33$
  • $HF = 32$
  • $HG = 58$
  • From this, we can find the measures for the unknown segments: $CD$, $CE$, $HD$, $GD$, etc.

Now moving to the second triangle $\triangle MNP$:

2. $T$ is the circumcenter of $\triangle MNP$

• Similarly, $T$ is equidistant from $M$, $N$, and $P$, meaning all of the distances from $T$ to these points are the same.

We need to express these values and solve any corresponding algebraic equations.

Would you like to proceed with a specific calculation for one of these segment measures, or do you have particular segments you'd like to focus on first? Let me know!