Central and Inscribed Angles - interactive applet
The properties of central and inscribed angles intercepting a common arc in a circle are explored using an interactive geometry applet. See also an analytical tutorial on inscribed and central angles in circles.
Consider a circle with radius r and a triangle ABC inscribed in it. The central angle BOC and angle BAC intercepts the same arc BC(see figure below).
Angle BOC is twice angle BAC.
Interactive Tutorial Using Java Applet
1 - Click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - Drag any of the vertices A, B or C to change the sides and angles of the triangle. Note That O is the center of the circumcircle of triangle ABC and angle BAC and BOC intercepts the same arc BC. Compare angle A and angle BOC. The ratio of angles BOC and BAC is also given.
3 - Drag two or more vertices to set angle A to 90 degrees (use the vertical and horizontal grid lines). Where is the center of the circle? Explain.
4 - Questions
a - Show that triangles ABO and ACO are isosceles triangles.
b - Use the fact that the sum of all angles in a triangle is equal to 180 degrees to write a relationship between the angles of triangles ABO and ACO .
c- Use the fact that the sum of all angle around point O is equal to 360 degrees.
d - Use the results of parts c and b to show that angle BOC is twice angle BAC.
Geometry Tutorials, Problems and Interactive Applets.