CabriProblemSolving

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Welcome to the problem solving pages of Cabri

Here You will find some Geometry problems, basic or advanced. If You are a Cabri user, we are interested in how You use it to explore, conjecture and prove. Please send us your report, and we will publish it in CabriSolutions. We hope to contribute in developing a problem solving culture in Dynamic Geometry.

Problems of the symetric-lateral triangle:

Defining the symetric-lateral triangle :

Let ABC a triangle and P a point. The symetric-lateral triangle of P about ABC is the triangle with vertex Pa, Pband Pc, reflections of P about BC, AC, and AB.

1. What is the locus of points P that have a right symetric-lateral ? (Solutions)

2. What is the locus of points P that have an isosceles symetric-lateral ? (solutions)(Solutions in Spanish) (Solutions in French)

3. What is the locus of points P that have an equilateral symetric-lateral ?(Solutions in Spanish) (Solutions in French)

4. What is the locus of points P that have a flat symetric-lateral ?

5. What is the locus of points P that have a symetric-lateral with the same area as the reference triangle ?(Solutions in Spanish) (Solutions in French)

6. To characterize the transformation that associates to each point P the barycenter of its symetric-lateral, and to give two different constructions of this transformation.

7.To characterize the transformation that associates to each point P the circumcenter of its symetric-lateral, and to give two different constructions of this transformation.

4/23/2004

Martin Acosta