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Incircle Inversion for Problem 5031

The incircle, its contact points, and the auxiliary intersections used in the inversion solution to Crux Mathematicorum Problem 5031.

Methods SVG construction

Triangle ABC with incircle contact points D, E, and F. A prime and C prime are the midpoints of EF and DE; P lies on DE and on the line through A parallel to EF; X is the intersection of A prime C and IP.
The incircle and auxiliary lines used in the inversion solution.Select the diagram to enlarge it.

This newly rendered figure records only the auxiliary construction used in the accompanying solution. It does not reproduce the original problem statement.