If ΔABC is isoscles with AB = AC and D, E and F are the feet of the angle bisectors of ΔABC, then what do you notice about the incentre I of ΔABC, the orthocentre H and circumcentre O of ΔDEF? Drag any of the vertices A or B to dynamically move and change the figure to check your observation.
Isosceles Triangle Collinear Conjecture
Can you explain (prove) your observation?
Related Links
False Collinear Conjecture
Triangle Incentre-Circumcentre Collinearity
Some Trapezoid (Trapezium) Explorations (see Investigations 3 & 4)
Parallelogram Distances (prove F, P, G and H, P, I are collinear)
Four Collinear Points
An interesting collinearity
Euler line proof
Further Euler line generalization
Euler-Nagel line analogy
Nine Point Conic and Generalization of Euler Line
Spieker Conic and generalization of Nagel line
More Properties of a Bisect-diagonal Quadrilateral
Quadrilateral Similar Triangles Collinearity
Investigating incentres of some iterated triangles
Investigating circumcentres of iterated median triangles
Four Collinear Points
Concurrency, collinearity and other properties of a particular hexagon
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Michael de Villiers, created 9 July 2011 with JavaSketchpad; updated to WebSketchpad, 11 July 2025.