Angle Formed by 2 Chords (V2): What Do You See?
- Tim Brzezinski
Recall that a CHORD is a segment whose endpoints lie on a circle. In the applet below, note that the purple angle is formed when the two chords intersect. This angle formed by two chords intercepts two arcs. One intercepted arc is red. The other intercepted arc is blue. There are two other angles shown as well. These are inscribed angles. The green inscribed angle intercepts the red arc. The brown inscribed angle intercepts the blue arc. Drag the green slider and carefully watch what happens. Feel free to move any of the points of the circle around to change the location of the purple angle formed by these two chords. As you move them, make sure that the 2 chords intersect each other! In addition, make sure that the green inscribed angle always intercepts the red arc and make sure the brown inscribed angle always intercepts the blue arc. After interacting with the applet for a few minutes, please answer the questions that follow (below).
Questions: ***Recall the Inscribed Angle Theorem (you've recently learned) to answer the following questions: 1) How does the measure of the green inscribed angle compare with the measure of its red intercepted arc? 2) How does the measure of the brown inscribed angle compare with the measure of its blue intercepted arc? ***Notice how the purple angle formed by the 2 chords intercepts the same 2 arcs (red arc and blue arc). 3) Given what you've observed in this applet, describe, in words, how you can find the measure of the purple angle formed by the two chords?