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The circumcenter of a obtuse triangle falls outside of its triangle?
always
The circumference of a triangle falls outside of its triangle?
always
Does the incenter of a triangle always falls outside of its triangle?
Never
What is the orthocenter of a triangle?
The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. An altitude extends from a vertex (i.e. corner of the triangle) to the side opposite of it, and is perpendicular either to the side of the triangle, or to its extension. The three altitudes of a triangle are always concurrent (intersect at the same point). This point is known as the orthocenter, and always falls on the Euler Line with the centroid, circumcenter, and the center of the triangle's nine-point circle.
What is The incenter of a triangle falls outside of its triangle?
The incenter of a triangle is the point at which the 3 medians (lines from the vertex to the middle of the side opposite the vertex) of the triangle intersect. Per it's definition, the incenter cannot ever fall outside the triangle. On the other hand, the orthocenter (intersection of the altitudes) can. It does so whenever the triangle is obtuse.
