If M is the circumcenter of ∆GHI, then;
GI = 61°
MH = 33.12
IK = 40.32
HI = 80.64
MG = 34.01
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. This point is equidistant from the three vertices of the triangle and is the center of the circumcircle, which is the circle passing through all three vertices of the triangle.
GJ = GL and JH = LI
GI = 31 + 30
GI = 61
Considering the right triangle MJH, the hypotenuse MH can be derived using Pythagoras rule as follows:
MH = √(14² + 30²)
MH = √1096
MH = 33.12
For right triangle IKM, MH = MI so;
IK = √(23² + 33.12²)
IK = 40.32
HI = IK + HK and IK = HK so;
HI = 40.32 + 40.32
HI = 80.64
For right triangle MJG, we derive the hypotenuse MG as follows;
MG = √(14² + 31²)
MG = √1157
MG = 34.01.
Therefore, the missing measures are; GI = 61°, MH = 33.12, IK = 40.32, HI = 80.64 and MG = 34.01.