For any point P inside a triangle, there is a corresponding point that can be found called its isogonal conjugate. To locate the isogonal conjugate, lines are drawn connecting angles to the selected point. These lines are then reflected across the angle bisectors. The reflected lines will cross at the isogonal conjugate of the original point. To find symmedians of a triangle, medians from each angle are reflected across the angle bisectors. The symmedians cross at the symmedian point, which is the isogonal conjugate of the centroid (the point where the medians cross).
To turn on lines, press the bubble next to the corresponding lettered line. Make sure to click the symbol next to the word "line" so all lines are accessible. 1. Turn on the grey lines d, e, and f. These are the angle bisectors of the triangle. 2. Turn on the blue lines g, h, and i. These are the medians of the triangle that intersect at the centroid G. 3. To find the symmedians, turn on the red lines g', h', and i'. These are the reflections of the medians across the angle bisectors. 4. Notice how the symmedians cross at point H. This is the isogonal conjugate of the centroid, G.