Download Inscribed and Central Angles

Project #7
This project is designed for a geometry classroom as an introduction to the relationship
between central and inscribed angles. Students should already have a basic
understanding of what a central angle is and what an inscribed angle is and how they
interact within a circle.
Directions:
1. Construct a circle. Label its center C.
2. Draw a point on the circle. Label it A. (You should now have two points on the circle, A and B.)
3. Construct central angle <ACB.
4. Locate 3 points on circle C in the exterior of <ACB and label them D, E and F. Construct the
inscribed angles <ADB, <AEB and <AFB. (To make this a little easier to see, try making each of
your angles a different color and getting rid of the labels for the sides of each angle. This really
seemed to help me.)
5. Measure each angle and put into the table below. (We want the measures of the angles to be
between 0 and 180. Make sure you record the correct measure in the table.)
m<ACB (1)
m<ADB (2)
m<AEB (3)
m<AFB (4)
Circle 1
Circle 2
Circle 3
6. Drag point A and record the measures for two more circles.
Conjecture:
1. How are angles 2, 3 and 4 related? Is this surprising? Notice where each of the angles intersects
the circle? Does the result make more sense now?
2. How do each of the angles above relate to the measure of angle 1? Can you make any guesses as
to why this might be true?
Extension:
The star divides the circle into congruent arcs. Use the conjecture you made above to find the
measures of the angles that form the points of the star (one of them is labeled x). Explain your
reasoning. Then measure each angle to verify your conjecture.