AMC 8 Daily Practice - Circles
Complete problem set with solutions and individual problem pages
To cultivate students' practical ability, the school's biology interest group set up a circular exhibition hall during the project-based learning "Making a Mini Ecosystem". As shown in the figure, a monitor is installed at point on the circular edge of the hall, and its monitoring angle is . To observe every position in the exhibition hall, what is the minimum number of such monitors that need to be installed on the circular edge?
- A.
- B.
- C.
- D.
- E.
The monitoring angle of the monitor (a circumferential angle) is , so the central angle corresponding to the arc it can monitor is:
To cover the entire circular exhibition hall (with a total central angle of ), the minimum number of monitors needed is:
Since the number of monitors must be an integer, we round up.
Thus, at least monitors are required.
