If a vertex, the , circumcenter, and the centroid of a triangle are ( 0, 0 ), (3, 4) and (6, 8) respectively, then the triangle must be
a. a right angles triangle
b. an equilateral triangle
c. an isosceles triangle
d. a right-angled isosceles triangle
Sol: Clearly, ( 0, 0 ), (3, 4) and (6, 8) are collinear. So, the circumcenter M and the centroid G are on the median which is also the perpendicular bisector of the side. So the triangle must be isosceles.
How did we come to know they're on the median and also the perpendicular bisector? (I couldn't understand it through the triangle I plotted. Please make a figure if that makes things easier)