ADVANCED CONSTRUCTIONS
1. hexagon inscribed in a circle
2. equilateral triangle inscribed in a circle (use the centroid as the center of the circumscribed
circle)
3. square inscribed in a circle
1. HEXAGON INSCRIBED IN A CIRCLE
NEW CONSTRUCTION
Construct a circle. Mark center O and point P on the circle. Measure the distance of the radius OP.
Beginning at P, mark off six arcs of the same length as the radius.
Connect the points of intersection to form a hexagon.
2. EQUILATERAL TRIANGLE INSCRIBED IN A CIRCLE NEW CONSTRUCTION
If given an equilateral triangle construct a circumscribed circle.
Construct the circumcenter by finding the perpendicular bisectors on two sides of the triangle. The
resulting circumcenter will also be concurrent with the centroid because it is an equilateral triangle.
The circumcenter / centroid is the center of the circumscribed circle and the segments joining the
center to each vertex is a radius. Hence, the cicumcenter is equidistant to the vertices.
If given a circle, construct the inscribed equilateral triangle. (Hint: use radius to identify the six points
on the circle –hexagon- and connect every other one to form an equilateral triangle.
3. SQUARE INSCRIBED IN A CIRCLE
NEW CONSTRUCTION
Given a circle construct a square inscribed in the circle.
Draw a diameter through the given center point.
Construct a perpendicular bisector of the diameter.
Connect the four points where the diameter and the perpendicular bisector intersect the circle to form
the square.
Given a square construct the circumscribed circle.
Draw the two diagonals of the square and use this point of intersection as the center of the circle.
Construct the circle.
REMEMBER TO REVIEW : Centroid Facts
* 2:1 ratio of the segment lengths of the median
* Find the centroid graphically by using midpoint formula between the vertices and reading the point of
 x1  x2 y1  y2 
,

2
2 
intersection on the graph M= 
