Question

The vertices of a triangle are (5, 1), (11, 1) and (11, 9). Find the co-ordinates of the circumcentre of the triangle.

Answer 1

Let the circumcentre be P (x, y).
Then, PA = PB
PA² = PB²
(x - 5)² + (y - 1)² = (x - 11)² + (y - 1)²
x² + 25 - 10x = x² + 121 - 22x
12x = 96
x = 8

Also, PA = PC
PA² = PC²
(x - 5)² + (y - 1)² = (x - 11)² + (y - 9)²
x² + 25 - 10x + y² + 1 - 2y = x² + 121 - 22x + y² + 81 - 18y
12x + 16y = 176
3x + 4y = 44
24 + 4y = 44
4y = 20
y = 5
Thus, the coordinates of the circumcentre of the triangle are (8, 5).