+128474 See the following image :
Let A = (0, 0) B = (10, 0)
We can find C thusly
Construct a circle with a radius of 21 centered at A
The equation of this circle = x^2 + y^2 = 441 (1)
Construct anothe circle with a radius of 17 centered at B
The equation of the circle is (x - 10)^2 + y^2 = 289 (2)
Subtract (2) from (1) and we get that
x^2 - (x - 10)^2 = 152
x^2 - x^2 + 20x - 100 = 152
20x - 252 = 0
20x = 252
x = 12.6 this is the x coordinate of C
And taking the positive value for y
y = sqrt (441 - (12.6)^2) = 16.8
So....C = ( 12.6 , 16.8)
The midpoint of AC = ( 6.3, 8.4)
The slope of the line between A and C is 8.4 /6.3 = 4/3
So...the equation of the perpendicular bisector to AC =
y = (-3/4) (x - 6.3) + 8.4
And the midpoint of AB = (5, 0)
So....the equation of the perpendicular bisector to AB = x = 5
This is the x coordinate of the center of the circumscribing circle
The y value is -.75 ( 5 - 6.3) + 8.4 = 9.375 = 9 + 3/8 = 75/8
So...the radius of the circumscribing circle is the distance from this point to A ans is given by :
sqrt (5^2 + (75/8)^2 ) = sqrt ( 1600 + 5625) / 8 = sqrt (7225) / 8 = 85 / 8
Answer: 85/8
