### How to generate graphs random geometric shapes?

I would like to create practice problems, rather than reusing old exam questions, to help my students practice solving geometric problems. I would like to use sagetex to produce random variations similar the questions I have listed below. I would supply examples of the pictures, but I do not have enough points to post pictures.

I am wish to be able to make one worksheet where each time it is printed, the values would be randomly assigned and graph would be produced. I know how to assign a random integer value to a variable; however, how to produce the graphs I have no understanding of how to achieve that. Thus for each of the example problems how to make the graph and how to assign the random variability to that graph.

**Example questions**

*The diagram below shows a childâ€™s toy which is made up of a circular hoop, centre O, radius 7 cm. The hoop is suspended in a horizontal plane by three equal strings XA, XB, and XC. Each string is of length 25 cm. The points A, B and C are equally spaced round the circumference of the hoop and X is vertically above the point O.*

- Calculate the length of XO.
- Find the angle, in degrees, between any string and the horizontal plane.
- Write down the size of angle AOB
- Calculate the length of AB.
- Find the angle between strings XA and XB.

*ABCDV is a solid glass pyramid. The base of the pyramid is a square of side 3.2 cm. The vertical height is 2.8 cm. The vertex V is directly above the centre O of the base.*

- Calculate the volume of the pyramid
- The glass weighs 9.3 grams per cm^3. Calculate the weight of the pyramid.
- Show that the length of the sloping edge VC of the pyramid is 3.6 cm
- Calculate the angle at the vertex, BVC
- Calculate the total surface are of the pyramid.