If H is the circumcenter, then each of EH, FH, and GH are perpendicular bisectors of the legs BC, CD, and DB, respectively. So, for instance, EH cuts BC in half so that BE and EC have the same length.
Also, BH, CH, and DH are radii to the circumcircle of the triangle, so they all have the same length.
(1) CD = CF + FD = 2 • FD = 2 • 32 = 64
(2) CE = BE = 26
(3) HD = HC = 33
(4) GD = 1/2 • BD = 1/2 • 58 = 29
(5) By the Pythagorean theorem,
HG² + GD² = HD²
so
HG = √(33² - 29²) = 2 √(62)
(6) Similar to (5); by the Pythagorean theorem,
HF² + FD² = HD²
so
HF = √(33² - 32²) = √(65)
