the logic of a construction
circumcircle and incircle of a triangle
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.
But then the question is raised how to do it and why use which lines for an circumcircle or an incircle.
An applet with a stepwise construction of the circles is a help of course
the logic of a construction
But why using wich lines?
And how to prevent confusing both constructions?
For students the logic is not always as clear as for teachers.
intuitive (soft) construction of circumcircle of a triangle
(Drag the three vertices of the triangle to change its shape.)
Drag the blue point to A.
Drag the centre (the red point) to different positions at which the circle also passes through B.
Observe the marks of these positions. What are their characteristic?
What is the charateristic of the positions of the centre at which the circle passes through A and C?
How to draw the circle which passes thorough A, B and C?
source: circumcircle (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.
Once the student gets the strategy he can try do do it on his own.