We call this the nosebleed section
By Stephanie Britt
Creating altitudes and orthocenters can be difficult to create but with the right script it can be created then maniputlated to test a specific hypothesis. Below is a script for one to use to do so. (must have Geometry Sketch Pad to view)
with this one can see the general view.
Point H is the orthocenter that helps create the orthocenters for Triangles ABH, BCH, and ACH. These new orthocenters are used to create the outer circles. The inner circle is the original Circumcircle.
Now let's explore what the relationship is between the altitudes of the original triangle using the image below as a reference.
What is
We can see that it equals 4, but what happens when the triangle vertices are shortened. We must keep the triangle and acute triangle but shortening the legs should not effect the measurement much right?
We can see that changing the leg lengths does not change the addition of the quotients. Explore this further to see what might change the number.
You can see for yourself that with the animation of all three points A, B, and C that the quotient will remain at 4 at all times.