Question

Suppose O, S, I, and G, respectively, denote orthocenter, circumcenter, incenter, and centroid of a triangle. Among the following situations, which is impossible in a triangle?

• A. O, I, and G are inside and S is outside it.
• B. O and S are outside while I and G are inside it.
• C. All these points are inside it.
• D. O and S are on the sides and I and G are inside it.

Answer 1

The correct option is A O, I, and G are inside and S is outside it.

In obtuse triangle, (2) is true.
In acute triangle, (3) is true.
In right triangle, (4) is true.
Hence, (1) is impossible.