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| c41 | Circle tangent to BC and externally tangent to the B- and C- excircles. |
| c42 | Inconic with focus P |
| c43 | Circumconic with focus F |
| c44 | Inconics through P, Q |
| c45 | Circumconics tangent to two lines L, L' |
| c46 | Point P with two cevians bounding a quadrilateral and a triangle having congruent incircles |
| c47 | Four congruent circles, three tangent to two sides and the fourth tangent to them |
| c48 | Point Q with circlecevian triangle inscribed in the circlecevian triangle of P |
| c49 | Inscribed triangle homothetic to the Morley triangle |
| c50 | Triangle inscribed in a circle and with sides going through three given points B, C, D (Castillon's problem) |
| c51 | Triangle inscribed in the circumcircle and triply perspective and orthologic to ABC |
| c52 | Given ABC, A', B', a point C such that ABC and A'B'C' be orthologic and perspective |
| c53 | Circle internally tangent to the excircles |
| c54 | Yff central triangle |
| c55 | Fourth common tangent to two inconics |
| c56 | Fourth intersection between a circumconic and the circumcircle |
| c57 | Axis of a circumconic |
| c58 | Axis of an inconic |
| c59 | Focus of an inconic |
| c60 | Inscribed triangles similar to the pedal triangle of a point Q |