Question

Find the circumcenter of the triangle ABC.
A( - 4,3), B(5,7), C(-4,7).

Answer 1

Circumcenter O (0.5 , 5)

Explanation:

Circumcenter O (x , y)

OA = OB = OC

OA² = (x + 4)² + (y - 3)²

OB² = (x - 5)² + (y - 7)²

OC² = ( x + 4)² + (y - 7)²

OA² = OC² : (x + 4)² + (y - 3)² = ( x + 4)² + (y - 7)²

(y - 3)² = (y - 7)² y² - 6y + 9 = y² -14y + 49

8y = 40

y = 5

OB² = OC² : (x - 5)² + (y - 7)² = ( x + 4)² + (y - 7)²

x² - 10x + 25 = x² + 8x + 16

18x = 9

x = 0.5

Circumcenter O (0.5 , 5)