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Construction [GSP files]

2.1 
Construction
of regular octagon: to construction a regular octagon by cutting corners
of a square. 
2.2

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

Partition of equilateral triangle
with four congruent incircles. 
3.1

Construction
2: Geomeric mean.

3.1

Solution of quadratic equations x(xa) = b^2
and x(ax) = b^2.

3.1.1

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

Harmonic
mean and the equation 1/a + 1/b = 1/x.

4.1

Construction
4: Archimedes' twin circles in the shoemaker's knife.

4.1

Constructions 5  6: Incircles of
shoemaker's knife.

4.2

Constructions 7  10: Four very simple
constructions of the incircle of a shoemaker's knife.

5.1

Euler's
formula for the distance between circumcenter and incenter of a triangle.

5.1.1

Construction 11: Given the circumcircle
(O) and the inradius r of a triangle, to construct the incircle.

5.1.2

Construction 12: Given the circumcircle (O) and
the incenter I of a triangle, to construct the incircle. 
5.1.3

Construction 13: Given the incircle
(I) and circumcenter O of a triangle, to construct the circumcircle.

5.1.4

Construction 14: Given the incircle
(I) and circumradius R of a triangle, to construct the circumcircle.

5.2.1

Construction 15: Given I in (O), to construct
(I) which is the incircle of quadrilaterals inscribed in (O).

5.2.2

Construction 16: Given (O) and r, to
construct (I) which has radius r and is the incircle of quadrilaterals inscribed
in (O).

5.2.3

Construction 17: Given (I) and O, to
construct (O) which is the circumcircle of quadrilaterals with incircle (I).

6.1

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.

6.2 
Construction 19: The two neighbors of a circle
tangent to (O) and to a chord BC at P.

6.3

Construction 20: Mixtilinear incircle.

6.4

Construction 21: Ajima construction of circle
tangent to the circumcircle of ABC and to PB, PC.

6.4.1

Thébault's theorem.

6.4.2

An animation picture of squares and circles.

7.1

Construction 22: To construct a triangle
given the length of one side, and the median and angle bisector on that
side.

7.2

Construction 23: To construct a triangle
given an angle and the corresponding median and angle bisector.

7.3

Construction 24: To construct a triangle given
a vertex, incenter, and orthocenter.
