7.1
Draw a circle with centre O and radius OA=1. Draw the diameters AA' and
BB', at right angles. With centres on the diameter BB' draw two circles, each
having radius of half that of the original circle. From point A swing an arc NM
which is tangent to the circumferences of the two inner circles. Repeat from
point A'. Construct square ACB'O from the radius of the original circle.
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7.2
The arc which lies tangent to the two inner circles cuts the outer unity
circle at exactly the point which gives the side of a regular pentagon
inscribed in the outer circle, measured from the extreme upper end of the
vertical diameter to the left at J and to the right at F. In addition, draw a
circle centred at A' and tangential to the near curve of the two inner circles,
we obtain the exact length of a third side of the pentagon, touching the outer
circle to the left at H and to the right at G. |
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7.3
Enclose the initial circle in a square. Then draw a circle by using the
centre of the initial circle as centre, and the distance to the tip of the
vesica as radius.
This circle will be equal in perimeter to the
perimeter of the square which is tangent to the initial circle. |
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