Department of Mathematics Education
Dr. J. Wilson, EMAT 6690
Constructing A Circular Window
by David Wise
Use a compass and ruler to construct the following design of
a circular window. How can it be constructed?
The key to this construction is to realize that the window
design is produced from three smaller congruent circles that are
all externally tangent to each other and internally tangent to
the large circular window.
- Construct an equilateral triangle. To do this, first construct
circle A passing through point B, then construct circle B passing
through point A. Construct the points of intersection (C and
D) of circle A and circle B. Construct segments AB, BC, and AC.
Triangle ABC is equilateral.
- Hide point D and circles A and B.
- Construct the midpoints (E, F, and G) of each side of triangle
- Construct the perpendicular bisectors of each side of triangle
ABC. Construct the intersection point (G) of the three perpendicular
bisectors (remember to select just two of the perpendicular bisectors
when constructing the intersection point to avoid the ambiguous
- Construct circle with center A passing through point G. Construct
circle with center B passing through E. Construct circle C passing
through point F. These three constructions produce the three
smaller congruent circles that are all externally tangent to
each other and will all be internally tangent to the large circular
- Construct the point of intersection (I) of line AF and circle
A. Construct the point of intersection (J) of line BG and circle
B. Construct the point of intersection (K) of line CE and circle
- Construct the large circle with center point H passing through
points I, J, and K. This is the large circular window.
- Hide lines AF, BG, and CE and triangle ABC.
- Construct arcs EFJ, FGK, and GEI.
- Hide circles the three smaller circles, so that only the
constructed arcs are visible. Hide all of the points that were
needed for the construction. The circular window design is now
Click here to investigate
the GSP sketch for yourself.
If you have any suggestions that would be useful, especially
for use at the high school level, please send e-mail to firstname.lastname@example.org.
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