In the classroom students learn stepwise the construction. In the best of all cases they go back home with a construction that's finished and correct.[br]But then the question is raised how to do it and why use which lines for an circumcircle or an incircle.[br][br]An applet with a stepwise construction of the circles is a help of course

But why using wich lines? [br]And how to prevent confusing both constructions?[br]For students the logic is not always as clear as for teachers.

([i]Drag the three vertices of the triangle to change its shape.[/i])[br][br]Drag the blue point to A.[br]Drag the centre (the red point) to different positions at which the circle also passes through B.[br]Observe the marks of these positions. What are their characteristic?[br][br]What is the charateristic of the positions of the centre at which the circle passes through A and C?[br][br]How to draw the circle which passes thorough A, B and C?

source: [url=https://tube.geogebra.org/material/simple/id/3958]circumcircle[/url] (by Anthony Or - Hong Kong)

A teacher knows the strategy: which lines to draw and why, but a lot of students don't. This applet helps the student discover the logic.[br]Once the student gets the strategy he can try do do it on his own.