Discovering Circles
Instructions
Introduction In this activity, you will construct, label, and experiment with a circle. In doing so, you will discover an important attribute of all circles. Step 1 Use the CIRCLE tool to create a circle with Point A as its center. Step 2 After you create the circle, you have a center point (A) and a point on the circle (B). The distance between these two points defines the radius of the circle. Use the DISTANCE tool to measure the radius of your circle. For this experiment we need to measure the diameter too. Challenge: Using the only tools available when you open the GeoGebra file, can you find a way to construct the diameter of your circle? Try it on your own first, but if you can’t find a way, use the See Hint…checkbox for the steps. Step 3 Use the DISTANCE tool to measure the diameter of your circle. By moving Point B to change the diameter of your circle, create five different circles and record the radius and diameter in the data table given below. Use a calculator to divide the diameter by the radius. Record this value in the third column on the data table.
Q1. Based on your observations, how would you describe the relationship between radius and diameter in words?
Q2. Can you write a rule or formula that connects the radius (r) and diameter (d)?
Q3. If you only know the diameter of a circle, how can you find the radius?
Q4. If a circle has a radius of 31.5 units, what is its diameter?