I give up. I've tried different ways and to no avail, can someone please check my work, tell me where I went wrong and point me to the right direction?

Coordinates X- (3,36)

Y- (66, 69)

Z- (97, 74)

P – midpoint of ZY,

P97 + 66,74 + 69

2 2

P163,1432 2

P ( 81.5 , 71.5 )

Q- midpoint of XZ,

Q3 + 97,36 + 74

2 2

Q100,110

2 2

Q (50 , 55)

R – midpoint of XY,

R3 + 66,36 + 69

2 2

R69,105

2 2

R (34.5 , 52.5)

Equation of line YR-

Y=mx + b

Y= 0.344x + b (97, 74)

Slope of line YR-

0.344

52.5 – 74=-21.5=

34.5 – 97 = -62.5 =

74 = 0.344 (97) + b

74 = 33.368 + b

b = 74 – 33.368

b = 40.632

Equation of line YR-

Y= 0.344x + 40.632

Slope of line YQ-

0.875

55 – 69=-14=

50 – 66 = -16 =

Equation of line YQ-

Y= 0.875x + b (66, 69)

69 = 0.875 (66) + b

69 = 57.75 + b

b = 69 – 57.75

b = 11.25

Equation of line YQ-

Y= 0.875x + 11.25

Equation of line XP-

Y = 0.452x + b ( 3, 36 )

Slope of line XP-

0.452

71.5 – 36=35.5=

81.5 – 3 = 78.5 =

36 = 0.452 (3) + b

36 = 1.356 + b

b = 36 -1.356

b = 34.644

Equation of line XP-

Y= 0.452x + 34.644

-y + (-0.875x) = -11.25

y – 0.452x = 34.644

0.423x=23.394

0.423 = 0.423

X= 55.305

Y – 0.452 (55.305) = 34.644

Y – 24.998 = 34.644

Y = 59.642

Point B – (55.305 , 59.642)

The coordinates of the circumcenter in triangle XYZ are (55.305, 59.642)