Collection 1 Topics: Conjugacies, Lines, Circles & Triangles

Every geometric transformation, central line, named circle, and derived central triangle encountered in Collection 1 (\(X₁\) through \(X_{19}\)) of the Encyclopedia of Triangle Centers.

Transformations & Conjugacies

• T_1 • Isogonal Conjugate
• T_2 • Isotomic Conjugate
• T_3 • Complement & Anticomplement
• T_4 • Harmonic Conjugate & Cross-Ratio
• T_5 • Circle Inversion

Named Central Lines

• T_6 • The Euler Line
• T_7 • The Nagel Line
• T_8 • The Brocard Axis
• T_9 • The Feuerbach Line
• T_10 • The OI Line (Incenter–Circumcenter Axis)
• T_11 • The Soddy Line
• T_12 • The Fuhrmann & Spieker Central Lines
• T_13 • The Isogonic & Napoleon Central Lines

Named Circles

• T_14 • The Incircle & Excircles
• T_15 • The Circumcircle
• T_16 • The Nine-Point (Feuerbach) Circle
• T_17 • The Spieker Circle
• T_18 • The Apollonian Circles
• T_19 • The Brocard & Orthocentroidal Circles

Derived Central Triangles

• T_20 • Medial & Anticomplementary Triangles
• T_21 • Orthic & Tangential Triangles
• T_22 • Intouch (Contact) & Extouch Triangles
• T_23 • Incentral & Excentral Triangles
• T_24 • Equilateral, Isogonic & Napoleon Triangles