Step 1. Construct segment AB.
Step 2. Construct circle A with radius AB.
Step 3. Construct AC, where C is a point on the circle.
Step 4. Measure angle CAB.
Step 5. Measure segment AB.
Step 6. We know there are 360 degrees in a circle. We must divide angle CAB by 360. This gives us the proportion of the sector to the circle.
Step 7. Calculate the area of circle A.
Step 8. Multiply the area of the circle times the proportion which gives us the area of the sector.
Why is this the area of the sector?
Step 9. Select the arc BC. Click Construct on the Menu bar and choose Arc Sector from the Arc Interior option.
Step 10. Select the sector and measure its area.
Compare the area in step 8 to the area of step 10.
Question:
Click on either of the points on the perimeter of the circle. Drag the point around the circle. Observe how the ratio changes. Make a conjecture.
Click Here for the GSP file.