GEOMETRY · CIRCLES · INVESTIGATION 08
Circle Tangent & Radius Explorer
Investigate the perpendicular relationship between a tangent and the radius at the point of contact.
Interactive mathematical workspace
Live simulationThe model updates as you adjust the apparatus controls. Values are simulated mathematical outputs, not physical measurements.
Primary result—
Secondary result—
Relationship—
Check—
Adjust a control to begin the investigation.
Learning objective
To investigate Circle Tangent & Radius Explorer using a dynamic mathematical model and justify a conclusion from recorded values.
Mathematical principle
Radius ⟂ tangent at point of contact
Procedure
1
Enter student details and note the initial settings.
2
Change one independent variable while keeping the others fixed.
3
Observe the visual model and note the calculated values.
4
Repeat with at least three different settings and record the readings.
5
Use the pattern in your observations to write a mathematical conclusion.
Variables
Independent: the control being changed. Dependent: calculated result. Controlled: other settings held constant.
Guided investigation: Rotate the tangent and observe the angle with the radius. A true tangent touches the circle at exactly one point.
Common errors to avoid
- Changing several variables simultaneously.
- Recording rounded values before completing calculations.
- Confusing linear, square and cubic units.
- Writing a conclusion that is not supported by observations.
Live mathematical analysis
Radius ⟂ tangent at point of contact
The working will appear here.
Observation table
| Trial | Settings | Result 1 | Result 2 |
|---|---|---|---|
| Run and record trials to populate this table. | |||
Compare the readings and identify the pattern.
Digital practical notebook
Recorded trials
| # | Settings | Result 1 | Result 2 | Time |
|---|
Knowledge check
Select the best answer. Feedback is provided after checking.
Assessment score0 / 5
Investigation challenge
Set the contact angle to 90°. Explain the radius–tangent relation.