If the orthocentre of a triangle is at (4,5) and the centroid is at (3,3), where is the circumcentre located? Answer is (2.5,2).

Please explain.

so.. centroid is dividing Orhtocentre and circumcentre in 2:1 internally
use section formula if the circumcentre is (x, y)

for X-coordinate:
3 = (4*1 + 2* x)/ 3 ….....(1)
9 =(4*1 + 2* x)
5 = 2 * x
so x = 5/2 = 2.5

for Y-coordinate:
3 = (5*1 + 2* y )/ 3
9 =(5*1 + 2* y)
4 = 2*y
so y = 2

so coordinates of circumcentre is ( 2.5 , 2)


thanks and regards