Centers of a Triangle
The Orthocenter (H) is the intersection of the three altitudes of a triangle.
The type of triangle determines where the orthocenter will be found.
In an acute triangle the orthocenter will be found on the inside of the triangle as in the picture below.
The orthocenter is the vertex of the right angle in a right triangle because the legs of the triangle are also 2 of the altitudes of the triangle.
In an obtuse triangle, the orthocenter is located outside of the triangle. It will be found on the altitude of the obtuse angle of the triangle.
It is also interesting to note that the altitudes and the orthocenter form triangles that have orthocenters related to the original triangle. The triangle ACH has an orthocenter at point B.
Likewise, the triangle BCH has an orthocenter at point A.
And triangle BHA will have an orthocenter at point C.