# Equilateral Triangles on Diagonals of Antiequilic Quadrilateral: What is this about?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2018 Alexander BogomolnyPlaying with the applet that demonstrates some properties of equilic quadrilaterals it is not hard to observe that the quadrilateral with two equal opposite diagonals inclined to each other at 120° also has interesting properties. As an HTML page needs to have a title relevant to its content, such a quadrilateral appeared to beg for a name. In deference to the origins of the shape I have named the quadrilateral *antiequilic*. Let ABCD be such an antiequilic quadrilateral

If equilateral triangles ACP and BDR are drawn on the diagonals AC and DB (towards AB) of an antiequilic quadrilateral ABCD, then their apexes P and R coincide. In addition, this point lies on the bisector of angle ASB, where S is the intersection of AD and BC.

What if applet does not run? |

### Equilic Quadrilateral

- Equilic Quadrilateral I
- Equilic Quadrilateral II
- Equilateral Triangles on Segments of Equilic Quadrilateral
- Equilic Quadrilateral I, A Variation
- Equilateral Triangles on Diagonals of Antiequilic Quadrilateral

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Copyright © 1996-2018 Alexander Bogomolny63408384 |