Arcs and Angles of Circles

Jenni McIntire and Teresa Davis


This lab is to explore central angles and inscribed angles and there intercepted arcs.

A central angle is an angle formed by two radii. A central
angle's vertex is on the center of the circle.

An inscribed angle is an angle whose vertex is on the
circle and whose sides intercept the circle.


Investigation:
In Sketchpad, make the following construction.

What is the relationship between the central angle and its inercepted arc? Move point C or D to see the relationship between the inscribed angle and its intercepted arc. What conjectures can you make


Investigation:
In Sketchpad, make the following construction.

Move point D around the circle. What do you notice about the measure of the angle? Can you explain why this is so?


Investigation:
In Sketchpad, make the following construction.

  • Construct circle A.
  • Construct secant CD where C and D are on the circle.
  • Construct point E on the circle and a line through E parallel to CD.
  • Construct the point of intersection of the new line and the circle and label it F.
  • Measure the arcs detween the parallel lines.
  • What do you notice about these measures? What conjecture can you make about the arcs between parallel lines? Move the points around, does your conjectur always remain true?


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