# 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.

 Review 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 Your browser is completely ignoring the tag! 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. More Geometry Tutorials, Problems and Interactive Applets.