Circle theorems are a set of fundamental principles in geometry that describe the relationships between angles, radii, chords, tangents, and other components of a circle.

These theorems form a crucial part of the study of Euclidean geometry and have numerous applications in fields such as engineering, architecture, and various sciences.

The working model of circle theorems provides a hands-on approach to exploring these relationships, making the abstract concepts more tangible and easier to comprehend.

Creating a working model to demonstrate circle theorems using cardboard and color paper is a great way to make these geometric concepts more tangible.

Here’s a step-by-step guide:

### Materials Needed:

- Cardboard or foam board
- Colored paper (different colors)
- Compass
- Ruler
- Pencil
- Scissors
- Glue or tape
- Protractor (optional)
- Marker

### Steps by Step Video Instructions:

#### 1. Prepare the Base:

- Take a piece of cardboard or foam board as the base for your model.
- Cut it into a large circle to represent the circumference of a circle.

#### 2. Draw the Circumference:

- Use a compass to draw a large circle on the cardboard.
- Alternatively, you can draw a circle by tracing a round object like a plate or bowl.

#### 3. Cut Out Shapes:

- Cut out various shapes from colored paper to represent different elements of circle theorems, such as chords, radii, tangents, and secants.
- You will need shapes like triangles, rectangles, and circles (for radii).

#### 4. Label the Shapes:

- Write labels for each shape to indicate what they represent (e.g., AB for a chord, O for the center, etc.).

#### 5. Create Theorems:

- Use colored paper to represent specific theorems.
- For example, for the theorem “The perpendicular bisector of a chord passes through the center of the circle”, create a chord and a perpendicular bisector.
- For “The angle subtended by a chord at the center is twice the angle subtended at the circumference”, create a chord and measure the angles.

#### 6. Attach the Elements:

- Glue or tape the shapes representing chords, radii, tangents, and other elements onto the circle base at appropriate positions.
- Ensure the positions are accurate and clearly labeled.

#### 7. Create Tangents:

- Use colored paper to create tangent lines that just touch the circumference at a single point.
- Glue or tape these tangent lines onto the circle.

#### 8. Demonstrate Theorems:

- Use the model to demonstrate various circle theorems.
- For example, demonstrate that the angle between a tangent and a radius is 90 degrees by measuring it with a protractor.

#### 9. Label and Explain:

- Write labels and explanations for each theorem directly on the cardboard base or on separate cards.
- Include the names of the theorems and brief explanations of their meanings.

#### 10. Add Decorations (Optional):

- Use markers or additional colored paper to add decorative elements to your model.
- For example, draw arrows to show the movement of lines or use different colors to distinguish different parts of the model.

#### 11. Display:

- Display your working model at the math exhibition or in the classroom where it can be easily seen by others.

With this model, you can effectively demonstrate and explain various circle theorems in an engaging and interactive way.