Inscribed Angles
Relationship between inscribed angles and its intercepted arc.
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle.
Watch the following video about inscribed angles. Pay special attention to how the measure of the intercepted arc was constructed, and how to construct and measure the inscribed angle.
Answer a few question about the video.
Which Geogebra tool was used to make the central angle hidden?
2.) What was the recommendation on the video for measuring an angle?
3.) How did the instructor get Geogebra to measure the arc?
Use this Geogebra applet to reconstruct the relationship between and inscribed angle and its intercepted arc. Make sure as you drag one of the endpoints of the arc, the measure of the arc and inscribed angle behave accordingly.
Question about your geogebra construction of an inscribed angle and intercepted arc.
1.) When you drag your endpoint of the arc to a measure of 80, what is the measure of the inscribed angle?
2.) What does the measure of the intercepted arc have to be for the inscribed angle to measure 60?
3.) Described the relationship between any inscribed angle and its intercepted arc. Please describe it in two different ways.