Question

Mathematics pls solve i need to check my answers bcs my teacher is sucky

Answer 1

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)