Jordan is the head of security at a famous casino hotel named The Compazu in Las Vegas. She decided to have a safe room constructed after a heist took place. About its design, the safe room will be circular, and three security cameras will monitor it. One of the cameras will be opposite the entrance door.
Place the compass at point B and draw another circle passing through point A. Then identify one of the intersection points of the circles as point C.
Connect the points using a straightedge.
Note that point A and point B are the centers of and respectively. Since passes through point B and passes through point A, the radii of the circles are equal. Therefore, AB, BC, and AC are equal. Consequently, △ABC is an equilateral triangle.
Given a circle, these three steps can be followed to construct a square inscribed in the circle.
Next, draw a segment perpendicular to AC at point O. This will be another diameter of Identify its endpoints as B and D.
Finally, by connecting the endpoints of the diameters, an inscribed square can be drawn.
The following steps can be followed to construct a regular pentagon.
Given a circle, begin by drawing an arbitrary diameter. Then identify the endpoints of the diameter as C and M.
Construct the perpendicular bisector of SO and identify the intersection point as L.
Next, draw a circle centered at point L with a radius of SL. Then draw a line passing through point M and point L intersecting From here, identify the intersection points of and the segment as N and P.
Now, two arcs centered at point M will be drawn. Both arcs will intersect One of them will pass through point P and the other one will pass through point N. Label the intersection points of the arcs and as A, E, B, and D.
Finally, connect points A, B, C, D, and E.
None of the previous constructions will help Jordan. Finally, by using a compass and a straightedge, a regular hexagon will be constructed hoping that it will help Jordan. Otherwise, she may lose her job.
These three steps can be followed to construct a regular hexagon inscribed in a circle.
Next, place the compass at point B and draw another circle passing through the center of Repeat the process until is intercepted six times and label the intersection points as C, D, E, and F.
Finally, connect the points using a straightedge.
Therefore, a regular hexagon ABCDEF has been constructed.
Among all of the constructions covered in this lesson, there is one in particular that will help Jordan place the cameras correctly — slowing any attempted heist! Recall that Jordan wants to determine the positions of the three cameras, given that one of the cameras will be opposite the entrance door.
According to the construction, each point on the circle is equidistant from each other. Therefore, it can be concluded that the distances between every other point are also equal.
Therefore, Jordan can determine the position of the cameras by choosing every other point starting from the position of the first point — Camera 1.
With this camera setup, Jordan can have three security cameras equidistant from each other, adequately monitoring The Compazu's safe room.