Question

find the coordinates of the circumcenter of the triangle whose vertices are(8,6) ,(8,-2)and (2,-2) also find the circumradius.

Answer 1

let it be (x,y)
therefore (8-x)² = (2-x)²
64 - 16x + x² = 4 - 4x + x²
64 - 4 = 16x - 4x
60 = 12x
x = 5

also,
(6- y)² = (y + 2)²
36 - 12y + y² = y² +4y + 4
36 - 4 = 12y + 4y
32 = 16y
y = 2

therefore, x= 5 , y = 2

Answer 2

circumcentre is a point of intersection of perpendicular bisector line
so , first of all construct triangle and now
step 1:-let A(8,6) B(8,-2) and c (2,-2)
mid point of AB (8,2)
mid point of Ac (5,2)
step2:-two point (8,2) and (2,-2) form equation and (5,2), (8,-2) form equation
step 3:-solve both equation and find answer
x=5 and y=2