There are three menu options, "Tangent to Arc/Circle/Function At Point", "Attach Point to Object", and "Control Buttons" under the "Misc" menu in a Euclidean session of Geometry Explorer.
In a Hyperbolic session there are three different options: "Point At Origin", "Base Pt of Triangle With Angles", and "Control Buttons".
Tangent to Arc/Circle/Function At Point: Use this option to construct a tangent to a circular object (arc or circle) at a point or to construct the tangent line to the graph of a function at a point on that function.
For example in the figure below we have constructed a circle and arc and have attached point P to the circle and point Q to the arc. (Recall: To attach a point to an object we use the point tool and click somewhere on the object). If we select P or Q, the menu option "Tangent to Arc/Circle/Function At Point" will be enabled under the "Misc" menu and choosing this option will cause the tangent line to be created.
Similarly, in the figure below we have constructed the graph of f(x) = x^2. (Look at the help page for the Graph menu for info on how to do this) We have attached point P to the graph. Once we select P we can then choose the tangent menu option resulting in the tangent line as shown.
Attach Point to Object: Use this option to attach a point to some object. First select the object and then choose this menu option.
Control Buttons: There are five different on-screen control buttons that one can create in Geometry Explorer. These buttons are activated by either double-clicking on the button or holding down the control key and clicking on the button.
Show/Hide Objects: Select a group of objects in the canvas and choose this option to create two buttons labeled "Show" and "Hide" on the screen. Activation of the button does what its name implies. Move Points: Select points in groups of two and choose this option to create a button named "Move". Activation of this button causes the first point in each group to move towards the second point until the tow points are coincident. Animate Point: Select a point that has already been animated and choose this option to create a button named "Animate". Activation of this button causes animation of the point to begin. Iterate Function: To create this button you must first define a function in the canvas. Then, select this function and choose this option to create a button named "Iterate". To use this button you must select a point that is attached to the function. Activation of the button will then cause the function to be iterated on the point. (Look here for an explanation of what function iteration is about) Sequence Function: Select a group of on-screen control buttons and choose this option to create a button named "Sequence". Activation of this button causes each button in the defining group of buttons to be activated in turn.
Point At Origin: In the Hyperbolic
Canvas it is often useful to create a point that is exactly at the
origin of the Poincare disk. To create this point just choose this
menu option under the "Misc" menu in a Hyperbolic Canvas.
Base Pt of Triangle With Angles: Use this option to aid in creating a specified hyperbolic triangle with a vertex at the origin and three given angles. To use this option first create a point at the origin and select it. This menu option will then be enabled under the "Misc" menu. Choosing it will cause the dialog box shown below to pop up. We set the three interior angles of the desired triangle in this dialog box. In the example shown, we are constructing a 45-45-45 triangle.
Once we hit the "Okay" button, a point will be created along the horizontal from the origin. This point is the correct second base point for the desired triangle. This is point B below.
To finish the definition of the triangle, we need to rotate point B about point O the desired angle, which in this case is 45 degrees. Once we do this and measure the angles we find that the triangle is indeed correctly constructed.
