Inscribed angels
Notice and Wonder:
What do you notice about the angle and the arc above? What do you wonder?
Discovery
Use the angle tool to find the approximate degree measure of . Write down your angle measure below.
Circle with central angle CAB
Mark a point D on the circle that is not on the highlighted arc from C to Q. Draw chords DB and DC. *Hint: Use the segment tool to connect the points.
Write down the measure of
Drag Point D to the right and to the left.
What do you notice?
Make a conjecture about the relationship between an inscribed angle and the central angle that is part of the same arc using what you discovered.
Now, try to place point D in another area on the circle.
Find the angle measures just like you did above.
Circle with central angle CAB
What do you notice different about the shape of the center angle and the inscribed angle from before? *If your shape looks familiar, try to discover a place to put point D that makes the shape look completely different.
Would have the same or different measures? Explain your answer.