# Euclid's Muse

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The Cyclic Quadrilateral Theorem states that for a quadrilateral inscribed in a circle, the measures of opposite angles must add to 180 degrees. Drag the points and observe the angle measures to see how this theorem holds true.

##### Euclids Elements - Book 2 - Proposition 14
One of my favorite apps because it looks deceptively simple, but takes some really creative thinking. This app creates a square (in red) that has the same area as a given quadrilateral.

Tags: Euclid, Elements, Geometry, Square, Quadrilateral

##### Epic Circle Trace 3
Four points are located proportionally around a circle, according to four different functions of t. A figure connecting the four points is traced through t. What are the four functions? Look at the .gx source for the answer. Tip: press "go" to animate t at a constant rate from 0 to ∏ and back, looped.

Tags: Proportional-point, function, circle, puzzler, trace, ellipse, sometimes-quadrilateral

##### Euclids Elements - Book 1 - Proposition 45
Creating a parallelogram equal to a given quadrilateral with a given angle.

Tags: Euclid, Elements, Geometry, Parallelogram, Triangle, Angle