1) I'm going to put this on a coordinate axis.
I place point A at the origin: A = (0,0)
I place point C at the point (16,0)
Since this is an isosceles triangle, point B will be somewhere above the midpoint of AC.
The distance from A to this midpoint is 8; the distance from A to point B is 17.
This makes an 8 - 15 - 17 right triangle, so point B = (8,15)
The circumcircle has its center at the intersection points of the perpendicular bisectors of the sides.
The line drawn from point B to the midpoint of AC is one of these perpendicular bisectors and its equation is x = 8.
Now, I plan to find the perpendicular bisector of AB and find where this line crosses the line x = 8.
The slope of AB is: (15 - 0) / (8 - 0) = 15/8.
This means that the perpendicular bisector of AB has a slope of -8/15.
The midpoint of AB is the point (4, 7.5).
The equation of the perpendicular bisector of AB is: y - 7.5 = (-8/15)(x - 4)
Multiplying this out: 15y - 112.5 = -8x + 32 ---> 8x + 15y = 144.5.
Now, to find where this line intersects the line x = 8: 8(8) + 15y = 144.5 ---> 15y = 80.5
---> y = 5.03125
This means that the circumcenter is (8, 5.03125)
To find the radius, I will find the distance from this point to the point (0,0):
distance = sqrt( (8.5 - 0)2 + (5.03125 - 0)2 ) = sqrt( 97.56347656 ) = 9.877422567.
I hope that this is clear and I hope that I didn't mess it up!