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Given a tangent with point of contact and the directrix, to construct the parabola.

Given the axis, focus, and one tangent, to construct the parabola.

Construct an animation displaying all possible parabolas tangent to a fixed circle having a fixed diameter as the axis.

Given the directrix and two points, to construct the parablas passing through the points.

Given 2 tangents and directrix, to construct the parabola.

Let a, b, c, d be given. Construct the graph of the function

((ax+b)x+c)x+d

Let a, b, c, d, e be given. Construct the graph of the function

Given k, a, b, c, d, construct the graphs of

k(x-a)(x-b),
k(x-a)(x-b)(x-c),
k(x-a)(x-b)(x-c)(x-d).

Given four points (x₁,y₁), (x₂,y₂), (x₃,y₃), (x₄,y₄), construct the graph of the cubic polynomial p satisfying

p(x₁) = y₁
p(x₂) = y₂
p(x₃) = y₃
p(x₄) = y₄

Construct the cardioid.

Construct the nephroid

Construct the deltoid.

Construct the astroid.

Construct the part of the tangent of the astroid intercepted by the curve

Two persons walk at constant speed around a circle. The ratio of their angular velocity is k ( k is not 0, 1 or -1). Find the envelope of all the straight lines joining them for k = 2, 3, -2, -3. Find the point of tangency

Construct the double generation of the deltoid.

Construct the double generation of the astroid

Construct the double generation of the cardioid.

Construct the double generation of the nephroid.

Construct the double generation of the rose curve of three leaves.

Construct the osculating circle of the astroid.

Construct the osculating circle of the cardioid.

Construct the osculating circle of the rose curve of three leaves.

Construct two mutually orthogonal tangents of the deltoid. Where do they meet?

Construct two mutually orthogonal normals of the deltoid. Where do they meet?

Construct a deltoid tangent to the sides of a given triangle.

Construct an animation displaying a deltoid sliding along two orthogonal straight lines.

Given a fixed deltoid, construct an animation displaying its circumscribed nephroid.

Given a fixed nephroid, construct an animation displaying its inscribed deltoid

Construct two identical cardioids each rotating about its cusp meeting orthogonally on the line segment joining the cusps.

Let AB be a fixed diameter of a circle O. Through a variable point C on O construct two cardioids with AB and BC as tangents and with the cusps at the distance of 2AB apart.

Construct an animation displaying two nephroids meeting orthogonally on a circle.

Construct the tooth-wheel coupling between the deltoid and the nephroid.

Construct the tooth-wheel coupling between the deltoid and the cardioid.

Construct the tooth-wheel coupling between the deltoid and the 4-cusped epicycloid.

Construct the tooth-wheel coupling between the deltoid and the 3-cusped epicycloid.

Construct the tooth-wheel coupling between the trochoids.

Construct the lemniscate with a linkage different from the previous one.

Demonstrate how the lemniscate can be drawn with the crossed parallelogram.

Construct two circles of the same radius with each rotating about a point not located at the center while remaining tangent to each other.

Construct two identical ellipses with each rotating about one of its two foci while remaining tangent to each other.

Design a linkage to draw the ellipse.

Demonstrate how the lemniscate can be drawn with the crossed parallelogram.

Construct Peaucellier's linkage converting straight line motion to circular motion.

Design a linkage to draw the cardioid.

Illustrate Pascal's Mystic Hexagram Theorem for a Circle: The points 12,
23, 31 of the intersection of the three pairs of opposite sides 1'2 and 12', 2'3
and 23', 3'1 and 13' of a hexagon 12'31'23' inscribed in a circle lie on a line.

Construct the conic passing through five given points.

Construct the conic passing through four given points and tangent to a given
line which contains one of the points.

Given three points and two lines each containing one of the points,
construct the conic passing through the three points and tangent to the lines
at the given points.

Illustrate Brianchon's Theorem for a Circle: If a hexagon is circumscribed
about a circle, the three joining pairs of opposite vertices are concurrent.

Construct the conic tangent to five given lines.

Construct the conic tangent to four given lines and passes through a point on
one of them.

Construct the conic tangent to three given lines and passes through two
points on two of them.

Construct a script which constructs the inversion of a circle given its center and a point on the circumference.

Construct an animation making the chain of circles move about the center.

Construct an animation illustrating Steiner's Porism: For any two (nonconcentric) circles one inside another, if circles are drawn successively touching them and one another so the last one touches the first, then it will always happen whatever the position of the first circle.

Investigate the various properties in the configuration of Steiner's porism for the chain of three circles.

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Construct the Poncelet's Porism in Poincare's Model.

Decompose an equilateral triangle into four pieces and reassemble them into a square.

Given two acute triangles S and T, show that each can be decomposed into three pieces

S = S₁ U S₂ U S₃
T = T₁ U T₂ U T₃

so that S_i is similar to T_i for i = 1,2,3.

Construct a linkage to draw the lemniscate after this design:

I.M. Yaglom, Geometric Transformation III, p. 15. Is there anything wrong?

This configuration was found in the Japanese temple. Make a dynamic animation out of it.

Construct the figure illustrating Morley's Theorem.

Explore the concurrent property in Morley's Theorem.

The similar concurrent property holds for the exterior case of Morley's Theorem.

What properties can be seen from this figure?