Paragraph
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Construction [GSP files]
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| 2.1 |
Construction
of regular octagon: to construction a regular octagon by cutting corners
of a square. |
2.2
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Given two congruent circles each passing through
the center of the other, to construct a circle tangent internally to one,
extenrally to the other, and also the line joining their centers. |
| 2.3 |
Construction 1: Equilateral triangle
inscribed in a rectangle: given a rectangle ABCD, to construct two points
P on BC and Q on CD such that triangle APQ is equilateral. |
2.4
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Partition of equilateral triangle
with four congruent incircles. |
3.1
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Construction
2: Geomeric mean.
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3.1
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Solution of quadratic equations x(x-a) = b^2
and x(a-x) = b^2.
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3.1.1
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Construction 3: Given a chord BC perpendicular
to a diameter XY of a circle, to construct a point A on the arc BYC such
that AX intersects BC at T with AT equal to a given length. |
3.2
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Harmonic
mean and the equation 1/a + 1/b = 1/x.
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4.1
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Construction
4: Archimedes' twin circles in the shoemaker's knife.
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4.1
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Constructions 5 - 6: Incircles of
shoemaker's knife.
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4.2
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Constructions 7 - 10: Four very simple
constructions of the incircle of a shoemaker's knife.
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5.1
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Euler's
formula for the distance between circumcenter and incenter of a triangle.
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5.1.1
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Construction 11: Given the circumcircle
(O) and the inradius r of a triangle, to construct the incircle.
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5.1.2
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Construction 12: Given the circumcircle (O) and
the incenter I of a triangle, to construct the incircle. |
5.1.3
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Construction 13: Given the incircle
(I) and circumcenter O of a triangle, to construct the circumcircle.
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5.1.4
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Construction 14: Given the incircle
(I) and circumradius R of a triangle, to construct the circumcircle.
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5.2.1
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Construction 15: Given I in (O), to construct
(I) which is the incircle of quadrilaterals inscribed in (O).
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5.2.2
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Construction 16: Given (O) and r, to
construct (I) which has radius r and is the incircle of quadrilaterals inscribed
in (O).
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5.2.3
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Construction 17: Given (I) and O, to
construct (O) which is the circumcircle of quadrilaterals with incircle (I).
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6.1
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Construction 18: Given P on a chord BC of
a circle (O), to construct the two circles tangent to (O) and to a chord
BC at P.
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| 6.2 |
Construction 19: The two neighbors of a circle
tangent to (O) and to a chord BC at P.
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6.3
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Construction 20: Mixtilinear incircle.
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6.4
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Construction 21: Ajima construction of circle
tangent to the circumcircle of ABC and to PB, PC.
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6.4.1
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Thébault's theorem.
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6.4.2
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An animation picture of squares and circles.
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7.1
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Construction 22: To construct a triangle
given the length of one side, and the median and angle bisector on that
side.
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7.2
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Construction 23: To construct a triangle
given an angle and the corresponding median and angle bisector.
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7.3
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Construction 24: To construct a triangle given
a vertex, incenter, and orthocenter.
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