Problems of Thébault
As problems of Thébault is referred to three problems from the elementary geometry by the French mathematician Victor Thébault were published (1882-1960). Since these are exclusively (in the meantime) proven statements, they are sometimes also referred to as Thébault's theorems, especially for the first and third problem, the term Thébault's theorem has become established in the literature.
Problem i
If you connect the centers of the squares built over the sides of a parallelogram, you get another square. This statement is also known as the Thébault-Yaglom theorem.
Problem ii
If equilateral triangles are erected over two adjacent sides of a square, their two corner points not lying on the adjacent square sides form an equilateral triangle with the corner point of the square not lying on the two adjacent square sides.
Problem III
If you connect a point on one side of the triangle with the opposite corner of any triangle, then there are two clearly defined circles that touch the connecting line, the side of the triangle and the circumference of the triangle. The centers of these two circles and the inscribed center of the triangle then lie on a straight line. This statement is also known as the Sawayama-Thébault theorem.
Web links
- Thébaults Problems and Variations on cut-the.knot.org