A=(3,3), B=(2,10), C=(9,11) Find the coordinates of the circumcenter and the radius of the circumscribed circle for △ABC.

Question

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Answer 1

midpoint of AB is (2.5,6.5) slope of AB is -7

perpendicular bisector equation is -x+7y=43

midpoint of AC is (6,7) slope of AC is 4/3

perpendicular bisector equation is 3x+4y=46

intersection of bisectors is circumcenter

Wow! they intersect at AC midpoint which is (6,7)

AC happens to be hypotenuse and angle B is 90 degrees

radius is distance from (6,7) to point A or point B or point C

radius is 5 units

Answer 2

Perpendicular bisector of AB: (x - 3)² + (y - 3)² = (x - 2)² + (y - 10)²; - 6x - 6y + 18 = - 4x - 20y + 104;

x - 7y = - 43;

Perpendicular bisector of BC: (x - 2)² + (y - 10)² = (x - 9)² + (y - 11)²; - 4x + 4 - 20y + 100 = - 18x + 81 - 22y + 121; 14x + 2y = 98; 7x + y = 49; x = 7y - 43; 49y - 301 + y = 49; 50y = 350; y = 7, x = 49 - 43 = 6

(6, 7) is circumcenter

It's radius R = √(7 - 3)² + (6 - 3)² = 5