An inscribed angle is an angle that touches the circle but opens inside the circle. Use the applet below to explore the relationship between an inscribed angle and a central angle which has a vertex on the center of the circle.

a. What relationship do you notice between the central angle ∠BAD and inscribed angle ∠BCD which intercepts the same arc?
b. Triangle CDA is an isosceles triangle, because sides AC and AD are both radii for the same circle. What relationship must exist between angles ∠ACD and ∠ADC?
c. Central angles ∠BAD and ∠CAD form a linear pair. How can you calculate the measurement of ∠CAD using ∠BAD?
d. All the angles of triangle CDA must add up to 180 degrees (angles ∠CAD, ∠ACD, and ∠ADC). Using your observations from (b) and (c) above, create a formula comparing the central angle ∠BAD and inscribed angle ∠ACD.
e. Suppose a central angle has a measurement of 180 degrees. What will be the measurement of an inscribed angle that intercepts the same arc?
f. Suppose an inscribed angle has a measurement of 42 degrees. What will be the measurement of a central angle that intercepts the same arc?