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Geometry figure library

A collection of Euclidean-geometry figures, with each configuration and its notation recorded clearly.

Two directly similar triangles OAB and OCD. Lines AE and DF meet at P, while AC and BD meet at Q. The points O, Q, and P are collinear. The two circumcircles have centers K and L, and OP is perpendicular to KL.

Pappus and Radical Axis for Problem 5021

The Pappus configuration and two circumcircles used in the generalized solution.

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.

Incircle Inversion for Problem 5031

The incircle and auxiliary lines used in the inversion solution.

Parallelogram ABCD with BC equal to BD and M the midpoint of CD. E, F, and G are the perpendicular feet from M to the lines BD, AD, and BC. The circle centered at M passes through E, F, G, and K; AK is tangent at K, and N is the intersection of EG and BM.

Tangent Circle in a Parallelogram

The circle centered at M and the auxiliary points used in the proof.

Cyclic quadrilateral BCAD with CB equal to CD. A₁ and B₁ are the altitude feet in triangle ABC; H bisects AA₁, and DB₁ is perpendicular to DB at D.

Cyclic Orthocenter Configuration

A representative configuration in which the two equivalent conditions hold.

Rectangle ABCD with M between B and C, N beyond C, perpendicular feet P and Q from B to AM and AN, and line PQ meeting BC at S and line AD at R.

Auxiliary Rectangle for a Fixed-Point Solution

The auxiliary rectangle and lines used in the solution.

ELEMENTARY GEOMETRY

Problems, Proofs, and Diagrams

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English edition · 2026