We have here a perpendicular bisector of GH, so it divides this segment into two equal parts, that is. GB = 8, and BH = 8.
We also have that the formed triangles BCG and BCH are congruent since GB is congruent to BH And they share the same side BC. The angles Therefore, we have:
GH = GB + BH ---> GH = 8 + 8 = 16
GC = CH = 12 (since we have congruent figures here.)
In summary, we have that
GH = 16
CH = 12