Friday, October 26, 2018

The Orthocircle. Who knew?

I have been writing some support materials for the yet to be released Pattern Blocks+ mathies tool. I received feedback that many elementary teachers would not be familiar with the term "altitude", much less "orthocentre". It occured to me, that I knew about the incentre and incircle, the circumcentre and circumcircle, but couldn't recall ever constructing an orthocircle.

I read Math is Fun's Triangle Centers page and loved the visuals and interactive sketches, but they did not include an orthocircle. The page says that there are actually thousands of "centres" of a triangle, and I wonder if "interior points" was what was meant.

After a little more surfing, I wrote the following:

The three altitudes of a triangle always intersect in a single point called the orthocentre of the triangle. This point is the centre of a circle that can be constructed by creating a triangle with sides parallel to the original triangle through its vertices (see below). 
A construction of the orthocircle of a triangle 
It was nice to dust off The Geometer's Sketchpad again.

Is the orthocircle as new to you as it was to me?
Is what I have written accurate or is it better to say that this is one of many orthocircles?

My 11th blog anniversary went by on the 23rd.