Orthocenter (& Questions)
Recall that 3 or more lines are said to be concurrent if and only if they intersect at exactly 1 point.
The ORTHOCENTER of a triangle is the point of concurrency of the LINES THAT CONTAIN the triangle's 3 ALTITUDES.
In the applet below, point O is the orthocenter of the triangle. Move the white vertices of the triangle around and then use your observations to answer the questions below the applet.
Questions:
1) Is it ever possible for a triangle's orthocenter to lie OUTSIDE the triangle? If so, under what circumstance(s) will this occur?
2) Is it ever possible for a triangle's orthocenter to lie ON THE TRIANGLE ITSELF? If so, under what circumstance(s) will this occur?
3) If your answer for (2) was "YES", where on the triangle did point O lie?
4) Is it ever possible for a triangle's orthocenter to lie INSIDE the triangle? If so, under what circumstance(s) will this occur?