The Complete Quadrilateral

Steve Phelps, 13/6/2014

Based on the work of John Wentworth Clawson (1881-1964) found in [b]The Complete Quadrilateral[/b]. You can access the paper at [url]https://archive.org/details/jstor-1967118[/url]. From Clark Kimberling's webpage [url]http://faculty.evansville.edu/ck6/bstud/clawson.html[/url] J. W. Clawson was probably the first to publish a description of an object in triangle geometry now known as the Clawson point. Born in St. John's, New Brunswisk, Canada, Clawson received the A.B. degree in 1901 from the University of New Brunswick. In 1905, he received the A.M. degree from Cambridge University. From 1907 until his retirement in 1952, Clawson was Professor of Mathematics and Physics at Ursinus College in Collegeville, Pennsylvania. During the last six of these years, he was Dean of the College. Clawson published a book of 63 pages - Geometry of Three Dimensions (Edwards Brothers, Ann Arbor, Michigan, 1938) - and several journal articles. The Clawson point originates in one of Clawson's problem proposals in the American Mathematical Monthly: no. 3132, submitted in 1925, and solved in v. 33 (1926), page 285.


  • 1. The Clawson Point
  • 2. The Complete Quadrilateral
  • 3. Four Triangles in a Quadrilateral
  • 4. Opposite Sides in a Quadrilateral
  • 5. Four Circumcircles in a Quadrilateral
  • 6. Four Circumcenters in a Quadrilateral
  • 7. Perpendicular Bisectors of Opposite Sides
  • 8. The Circumcentric Circle
  • 9. Tangents to the Circumcircles
  • 10. Vertices and Midpoints
  • 11. Diagonals of the Complete Quadrilateral
  • 12. Diagonals and Derived Quadrilaterals
  • 13. Points on the Circumcentric Circle

1.

The Clawson Point

The Clawson Point The Clawson point is the homothetic center of the orthic triangle A'B'C' and the extangents triangle A''B''C''. In the figure, the reference triangle is labeled ABC. Its orthic triangle, A'B'C', is formed by the feet of the altitudes of triangle ABC - for example, A' is the point in which the altitude through A meets side BC. The extangents triangle, labeled A"B"C", is formed by the lines externally tangent to the excircles of triangle ABC. The lines A'A", B'B", C'C" concur in the Clawson point of triangle ABC. Only points A, B, and C are draggable. [url]http://faculty.evansville.edu/ck6/tcenters/recent/clawpt.html[/url]
– Steve Phelps

2.

–

3.

–

4.

–

5.

–

6.

–

7.

–

8.

–

9.

–

10.

–

11.

–

12.

–

13.

–

Información