A point M in the segment determines then two lengths adding up to the total rope length. Taking these two lengths as the radii of two circles around the points A and B (the sticks) we just have to consider one intersection point as the tracer point and apply the locus function to get one branch of the ellipse as illustrated in Fig. 1. Following the instructions mentioned above, a webDiscovery .txt file is created from the textual description of the construction in the Java Sketchpad .html file. If this file is uploaded to the application, the answer returned by LAD says that the equation of the locus is a conic (in u(9) and u(10)) and it provides the exact symbolic equation with 115 summands! This is in fact the general equation for the ellipse considering two general foci and a general length. However it is most definitely too much information for a student in a Math lab. To simplify things we can assign numeric coordinates to the free points in the construction. In particular, if we assign the coordinates (1,1), (3,1), (0,0), (1,0) to the points E,D,B and A respectively, and upload the modified file to the application we obtain the answer as a simple quadratic equation (see Fig. 1, right).
Let us note that due to the algebraic nature of LAD, the equation provided corresponds to the whole ellipse (not just one branch). Observe the reference to the conditions that the point T has to satisfied. In this case there are no required conditions since it is a parametric and not an implicit locus.
After pasting the Cabri textual description of the construction in the applet, we select Find a LOCUS from the applet menu and add the condition Equidistance for the points T, B and Af. Finally we also have to specify T as the tracer point. Pressing the To OM and the To wD buttons generates the webDiscovery description of the task with symbolic variable assigned to the free points in the construction. If we upload the .txt file with that description, the answer returned by LAD says that Af is the midpoint of the segment BT only if T lies in a conic whose exact symbolic equation is provided (see Fig. 2, right up).
Like in the previous example, we can assign numeric coordinates to free points to obtain the answer to a convenient particularization of the question. We assign numeric coordinates so the vertices A and B become the points (0,0) and (1,0) (see modified file). For this particular case the answer says that T has to be in the circle with center B and radius equal to the distance AB (see Fig. 4, right down).
After pasting the GSP textual description of the construction from the .html file in the upper left text area in the applet, we select PROVE from the applet menu and add the condition Incidence for the point P and the line L10. Let us recall that GSP does not keep the line labels in its .html file. The assigned name of the last constructed altitude is L10 because it appears in the line numbered as 10 in the .html file. The name can also be looked up in an OpenMath description of the construction (obtained by pressing the To OM button). Once the condition to prove has been added, one just have to press the To OM and the To wD buttons to generate the webDiscovery description of the task. Uploading the .txt file to the application, the answer is obtained (see Fig. 3, right).
After pasting the Cinderella textual description of the construction (from the file obtained after decompressing the .cdy file) in the applet, we select DISCOVER from the applet menu and add the condition Collinearity for the points A, O and C. Once the condition to discover has been added, one just have to press the To OM and the To wD buttons to generate the webDiscovery description of the task. Uploading the .txt file to the application, the answer is obtained (see Fig. 4, right). As expected, the condition is that we have right triangle. Note that LAD also gives the degeneracy condition A = C.
