Question

Find the circumcenter of a triangle whose vertex are (8, 6) (8 -, 2 ) and ( 2 - 2)

Answer 1

: Let the coordinates of the circumcentre of the triangle be (x, y).Circumcentre of a triangle is equidistant from each of the vertices. Distance between (8, 6) and (x, y) = Distance between (8, -2) and (x, y) √[(x - 8)2 + (y - 6)2] = √[(x - 8)2 + (y + 2)2] [(x - 8)2 + (y - 6)2] = [(x - 8)2 + (y + 2)2] (y - 6)2 = (y + 2)2 y2 + 36 - 12y = y2 + 4y + 4 36 - 12y = 4y + 4 16y = 32 y = 2 Distance between (2, -2) and (x, y) = Distance between (8, -2) and (x, y) √[(x - 2)2 + (y + 2)2] = √[(x - 8)2 + (y + 2)2] [(x - 2)2 + (y + 2)2] = [(x - 8)2 + (y + 2)2] (x - 2)2 = (x - 8)2 x2 + 4 - 4x = x2 - 16x + 64 4 - 4x = -16x + 64 12x = 60 x = 5. Hence, the coordiantes of the circumcentre of the triangle are (5, 2). Circumradius = √[(5 - 8)2 + (2 - 6)2] = √(9 + 16) = √25 = 5 units.