The locus of the orthocentre (1)
In the following drawing, the orthocentre H of a tringle ABC is constructed. The triangle's vertex C is bound to a circle k. When you run C along its "carrier line" k, then the point H runs on a line that is completely determined by the positions of A, B and k. The drawing holds a picture of this line; it is called a locus line of the point H.
When you drag C along k this has no effect on the locus line but only on the actual position of the orthocentre H. But you can also drag A or B to a new position, or make changes to the centre and radius of k. In every case not only the triangle ABC and its orthocentre are updated correctly, but furthermore, the locus line of H is recalculated and updated, too!
But, this drawing also shows the limitations of EUKLID DynaGeo's implementation of locus lines. In special situations it may be that the line drawn does not coincide with the true positions of the orthocentre. (It is intentionally left to you to find out the conditions for this fault to happen!) This is due to the fact that DynaGeo's locus lines are internally constructed as Bezier curves through a certain number of correctly calculated positions of H. But if the gaps between these points become too big, DynaGeo must guess about the path of the locus line between these points - and sometimes a guess can miss! So, the line shown is only a numerical approximation of the true locus line!
