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).

perpedicular bisectors of a segment

Angle BOC is twice angle BAC.

Interactive Tutorial Using Java Applet

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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.