Question

G is the centroid, S is the circumcenter, and O is the orthocenterof a triangle. O divides GS externally in the ratio of

• A. 2 : 1
• B. 3 : 2
• C. 3 : 1
• D. 4 : 3

Answer 1

The correct option is B 3 : 2

For a given triangle the relation between the centroid G,
the circumcenter S and the orthocenter O is:
2SG = GO
These three points are always colinear.
eg,
if the coordinates o f the points are : O(0,0) , G(0,2), S(0,3)
(since 2SG = GO), then O divides the line joining G and S externally in the ratio OS:OG i.e.
3:2