Day 3: Circle Arcs

Review: A central angle of a circle is an angle with its vertex at the center of that circle. In the diagram below, angle A is a central angle. The measure of angle A equals the measure of arc CD. (We say that angle A intercepts arc CD.)

Question: In the diagram below, the measure of arc CD equals the measure of arc EF. What is true about angles DAC and EAF? Why?


Construct a circle A, then construct four points on the circle. Label these points C, D, E and F. Construct chords CD and EF. Construct arcs EF and DC. (To construct arc EF, click on point E, click on the circle, click on point F and choose "Arc on Circle" from the Construct menu at the top of the page. (By the way, we say that chord EF subtends arc EF.) Measure lengths EF and DC, then measure arc angles EF and DC. Drag various points until chords EF and DC are congruent. What appears to be true? Proof? Hint?