Find the coordinates of the circum centre of the triangle whose vertices are 0 0 8 0 and 0 6 Find th......

Find the coordinates of the circum-centre of the triangle whose vertices are (0, 0), (8,0) and (0,6). Find the Circum-radius also.

Circum-centre is the point of intersection of the perpendicular bisectors of the three sides of a triangle.
Let S (x, y) be the circumcentre.
SA = SB = SC. ∴ &redic;(x² + y²) = &redic; (x-8)² + (y-2) )².
&redic;(x² + y²) = &redic; (x-0)² + (y-6) )².
Squaring x² + y² = x² – 16x + 64 + y². So x = 4.
Also x² + y² = x² + y² – 12y + 36.
So y = 3. Hence coordinates of the circumcentre is (4, 3).
Circumradius = SA = &redic; x² + y = & redic;16+9 = 5.
=> (3,4),5

By: Amit Kumar