Inscribed Angle Theorem (Intro): What Do You See Here?
Recall that in a circle, an INSCRIBED ANGLE is an angle whose vertex lies on the circle and has rays that intersect the circle at two distinct points. In the applet below, the blue angle is an INSCRIBED ANGLE that intercepts the red arc. The red angle is a central angle (of the circle) that also intercepts the same red arc. In fact, this applet was designed so that both the inscribed angle and central angle always intercept the same red arc. 1) Drag the green slider all the way to the right in the applet below and watch what happens. 2) Now drag the slider all the way back. Move any one or more of the blue and/or red points around and repeat step (1). 3) Repeat step (2) as many times as desired. Answer the questions that follow.
Questions: 1) How does the measure of any central angle of a circle compare with the measure of its intercepted arc? 2) According to what you've observed in the applet above, how does the measure of the inscribed angle compare with the measure of the central angle (that intercepts the same arc?) 3) Use your results from (1) and (2) to describe how one could find the measure of an inscribed angle given the measure of the arc it intercepts.