Inscribed and Central Angles
Use this applet to discover and prove the relationship between inscribed and central angles.
1. Make a conjecture about the relationship between the central and inscribed angle, just be dragging around the points B and C.
2. Click show Relationship between △CAB and △COB and refine your conjecture.
3. Click show triangles. Looking at the triangles, what is in common about segments CO, AO, and BO?
4. What type of triangles are ACO andABO?
5. Click Show angles and refine your answer from part 4 if you need to. What are the angles ∠COA and ∠COB in relation to the two angles, let them be x and y respectively, shown of each triangle?
6. Click More angles and refine your answer from part 5 if you need to. Now using that fact that a circle is 360what is the angle ∠BOC?
7. Click Final Angles and refine your answer from part 6 if you need to. Now in terms of x and y what is the inscribed and central angles.
8. How does this prove the conjecture you formed in part 1?