Interactive Geometry

By default, use the first link in each construction; it points to a GeoGebra applet. Some of these constructions are equivalent to the exercises in Euclidea — a cool collection of interactive geometric puzzles. If you need to use C.a.R. applets, read the instructions at the bottom of the page.

Test construction (in C.a.R.).
Congruent triangles
- Copy of triangle.
Perpendicular lines
- Angle bisector (in C.a.R. or 2.1 in Euclidea).
- 5.22. Perpendicular ( in C.a.R. or 2.6 in Euclidea).
- 5.23. Center of the circle ( in C.a.R. or 1.6 in Euclidea).
- 5.24. Tangent to the circle ( in C.a.R.).
- 5.25. Tangent circle ( in C.a.R.).
Parallel lines and similar triangles
- 7.5. Parallel line ( in C.a.R. or 5.1 in Euclidea).
- 7.11. Segment trisection ( in C.a.R. or 10.6 in Euclidea).
- 7.27. Apollonian circle ( in C.a.R.).
Triangle geometry
- Circumcircle ( in C.a.R. or 7.6 in Euclidea).
- Incircle ( in C.a.R. or 7.7 in Euclidea).
Inscribed angles
- 9.9. Right angles (in C.a.R.).
- 9.11. Perpendicular with ruler (in C.a.R.)
- 9.20. Equal angles (Equal angles)
- Triangle with given base, perimeter and angle (in C.a.R.)
Inversion
- 10.5. Inversion
- 10.22. Perpendicular circles
- 10.23. Perpendicular to 3 circles
Hyperbolic plane
Affine geometry
- (14.5.) Segment bisection
- Affine segment trisection
- 14.6. Arithmetic construction
- 14.7. Center with parallel tool
Projective geometry
- (15.8.) Three pairs of parallel lines
- 15.15. Third parallel line or 11.5 in Euclidea
- (15.18.) Tangents to the circle with ruler
- 15.19. Center of concentric circles
- Intersection point (in C.a.R.).
Spherical geometry
- Spherical perpendicular
- Tangent great circle
Geometric constructions

The C.a.R. applets are written in Java. Since in all major browsers the support for Java plugins has ended, we recommend installing Java Developers Kit (JDK 8) (or OpenJDK 8) and open the exercises using the command appletviewer url... For example, to open the first exercise, you use the following command:

appletviewer http://anton-petrunin.github.io/birkhoff/car/Angle%20bisector.html

On Windows, before executing the command, you may need to navigate to the folder with appletviewer; it should be something like C:\Program Files\Java\jdk1.8.0\bin

If your computer has a more recent JDK, you might need to force it to use the older JDK by entering export JAVA_HOME=$(/usr/libexec/java_home -v 1.8) (or something like that) before executing appletviewer.