Switch to the *geometric tab* using the _{} button.

We will create an equilateral triangle which side length is *a* and calculate its altitude.

In the *geometric tab* menu, choose **Create Object** then **Point** and **Coordinated Point** (**Create Object** / **Point** / **Coordinated Point**).

Figure 17 - Menu Create Object / Point / Coordinated Point

A *dialogue box* opens, for x enter 0 and for y, a. Click on **Create** and **Exit**.

Figure 18 - Coordinated point creation box

Figure 19 - First point in geometry tab

To name a point, right-click on it. A *box* opens, with the drop down menu, you can choose a letter name and you can choose the name’s position. Name the new point B.

Figure 20 - Point properties box Figure 21 - Point B

We will create two circles: **Create Object** / **Circle** / **Circle by Center and passing through a Point**. The first circle is by centre o and passing through the point B, the second is by centre B and passing through the point o.

Figure 22 - First circle Figure 23 - Second circle

Now we will create the two circle intersection points: **Create Object** / **Point** / **Intersection of two Circles**. Select one of the circles then the second. It creates the two points. Name them C and D.

Figure 24 - Intersection points C and D

We will create the segment [oB]: **Create Object** / **Line** / **Segment**. Select the point o or B then the other point. It creates the segment.

Figure 25 - Segment [oB]

Create the point middle H of segment [oB]: **Create Object** / **Point** / **Point Middle**. Select the segment [oB]. Name the point H.

Figure 26 - Middle point H

Switch to the *geometric calculation tab* (_{} button).

Consider the BoC triangle. Each radius circle measures *a*, so Bo, oC and CB measure *a*. Boc is an equilateral triangle. To measure its altitude: CH, create the geometric calculation CH. Click on **Create Calculation**. In the *box*, in *Calculation box* enter *CH*. Click on **Create** then **Exit**.

Figure 27 - Creation of geometric calculation CH

In the *geometric calculation tab*, Casyopée created the calculation *c0*. When one checks the calculation, one can observe an approximate value. How does this value depend on *a*?

Figure 28 - Figure and calculation when *a* = 4

In the toolbar, change the value of *a*. Observe that circles’ radius and the resulting change of c0.

Figure 29 - Figure and calculus when *a* = 9

The value of CH could depend on *a*. To verify this hypothesis, highlight the calculation, choose **Dependance**. A *box* opens, it says that “The calculation depends on no free point” and suggests to export as an expression. Choose **Yes**.

Figure 30 - Calculation exportation box

Another *box* opens and gives the new geometrical expression. It is depending on *a*. Click on **OK**.

Figure 31 - Box "New geometrical expression"

Go back into the *expression list* (with _{} button), observe the new expression E, which gives the altitude of an equilateral triangle whose side is *a*.

Figure 32 - Expression E of the altitude of an equilateral triangle whose side is *a*

**22/11/2014 - 21h51**

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