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8.2 Inscribing shapes in circles

8.2 Inscribing shapes in circles

An inscribed shape is one that !ts inside a circle with all its vertices (corners) touching the
circumference of the circle. You must be able to inscribe squares, equilateral triangles, regular hexagons
and octagons by constructing equal divisions of a circle, using only a straight edge and compasses.

Worked example 8.2

Draw a circle with a radius of 4 cm. Using a straight edge and compasses, construct an inscribed:
a square b regular octagon c equilateral triangle d regular hexagon.

a Step 1 Start by drawing a circle Step 2 Draw a diameter
with radius 4 cm. Mark of the circle on the
4 cm
the centre of the circle diagram.
with a small dot.

Step 3 Using compasses, Step 4 oin the ends of
J

construct the the two diameters,
perpendicular bisector of in order, to form a
the diameter. Extend it to square.
form a second diameter.

b Step 1 Start by drawing a circle Step 2 Draw a diameter
with radius 4 cm. Mark of the circle on the
4 cm
the centre of the circle diagram.
with a small dot.

Step 3 Using compasses, Step 4 Construct the angle
construct the bisector of one of the
perpendicular bisector of right angles (90°) at
the diameter. Extend it to the centre of the circle
form a second diameter. and extend it to form
a third diameter.

J
Step 5 Construct the angle Step 6 oin the ends of
bisector of one of the the four diameters,
other right angles at in order, to form a
the centre of the circle regular octagon.
and extend it to form a
fourth diameter.

78 8 Constructions and Pythagoras’ theorem