The Euler lines of triangles ABC, AIC,
BIC, and AIB respectively, where I is the incenter of ABC,
concur at the Schiffler point S.
O, O1, O2, O3 and G, G1, G2, G3 are the circumcenters and centroids of triangles ABC, AIC, BIC, and AIB
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on the figure to start the animation.
Drag points A, C and line AC to change
Euler Line is the line through the centroid,
circumcenter and orthocenter of a triangle.
Centroid is the concurrent point of the medians of a
Circumcenter is the concurrent point of the perpendicular
bisectors of a triangle.
Orthocenter is the concurrent point of the altitudes of a
Incenter is the concurrent point of the angle bisectors
of a triangle.
Concurrent: Two or more lines are said to be concurrent
if they intersect at a single point.
Kurt Schiffler (1896-1986), an accomplished amateur
geometer, discovered one of the most attractive of the
"twentieth-century" triangle centers, now known as the Schiffler
point. He introduced the point in the Mathematicorum problem
Reference: Schiffler, Kurt; Veldkamp, G. R.; van der Spek,
W. A. (1985). "Problem 1018". Crux Mathematicorum 11: 51.
Solution, vol. 12, pp. 150–152.
Dynamic Geometry: You can alter the figure above
dynamically in order to test and prove (or disproved)
conjectures and gain mathematical insight that is less
readily available with static drawings by hand.
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TracenPoche is a project of Sesamath, an association of French
teachers of mathematics.