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.
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 AND where on the triangle will point O lie?
3) Is it ever possible for a triangle's orthocenter to lie INSIDE the triangle? If so, under what circumstance(s) will this occur?