Griffiths' theorem

File:Pedal circle griffith point2 schar.svg

Griffiths' theorem, named after John Griffiths (1837-1916), is a theorem in elementary geometry. It states that all the pedal circles for a points located on a line through the center of the triangle's circumcircle share a common (fixed) point. Such a point defined for a triangle and a line through its circumcenter is called a Griffiths point.{{MathWorld|title=Griffiths' Theorem|urlname=GriffithsTheorem|mode=cs2}}

Griffiths published the theorem in the Educational Times in 1857. Its later rediscoveries include works by M. Weil in Nouvelles Annales de Mathématiques, 1880, and by W. S. McCay in Transactions of the Royal Irish Academy, 1889.{{citation|title=Advanced Euclidean Geometry|publisher=Houghton Mifflin|year=1929|page=245|first=Roger A.|last=Johnson}}; reprint, Dover Books, 1960.{{citation

| last = Tabov | first = Jordan

| issue = 1

| journal = Mathematics Magazine

| jstor = 2691382

| mr = 1573071

| pages = 61–64

| title = Four Collinear Griffiths Points

| volume = 68

| year = 1995}}

Additionally, in 1906, {{Interlanguage link|Georges Fontené|fr|Georges Fontené}} refound the theorem.{{Cite book|author=G. Fontene|title=Sur le cercle pédal |year=1906 |publisher=Nouvelles annales de mathématiques |pages=508-509 |url=http://www.numdam.org/item/NAM_1906_4_6__508_0.pdf}} So the theorem is also called the Fontené's (Second) theorem.{{MathWorld|title=Fontené Theorems|id=FonteneTheorems}}