Triangles, Quadrilaterals
and Circles

This page is a sub-page of our page on Geometric Shapes.

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Related KMR-pages

• …

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Other relevant sources of information:

Plane geometry
Interactive Quadrilaterals
A miracoulus proof of Ptolemy’s Theorem, Zvezdelina Stankova on YouTube

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The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.

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The centroid of a triangle:

Triangle - centre of gravity

Interactive simulation of the centroid of a triangle.

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The circumscribed circle of a triangle:

Triangle - circumscribed circle

Interactive simulation of the circumscribed circle of a triangle.

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The inscribed circle of a triangle:

Triangle - inscribed circle

Interactive simulation of the inscribed circle of a triangle.

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The orthocentre of a triangle:

Triangle - orthoCentre

Interactive simulation of the orthocentre of a triangle.

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The Simpson line of a triangle:

The interactive simulation that created this movie.
(dragable points).

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The tangential circles of a triangle:

Triangle - tangential circles

Interactive simulation of the tangential circles of a triangle.

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Napoleon’s theorem:

The interactive simulation that created this movie.

Interactive simulation of Napoleon’s theorem

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Thebault’s theorem:

The interactive simulation that created this movie.

Interactive simulation of Thebault’s theorem.

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Desargues’s theorem:

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The nine-point circle of a triangle:

The interactive simulation that created this movie.

Interactive simulation of the nine-point circle of a triangle.

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The Euler line of a triangle:

The interactive simulation that created this movie.

Interactive simulation of the Euler line of a triangle.

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Morley’s trisector theorem

Many Morley triangles

The Morley-Naeve triangle:

The interactive simulation that created this movie.

Interactive simulation of the Morley-Naeve triangle.

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Pappus’ area theorem:

The interactive simulation that created this movie.

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Pythagoras’ theorem:

The interactive simulation that created this movie.

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Complete Quadrangle:

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But why is a sphere’s surface area four times its shadow? (Steven Strogatz on YouTube):

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