Synthetic and Vector Proofs for Two Hard Geometry Problems | Synapse
June 8, 2026Open Access
Synthetic and Vector Proofs for Two Hard Geometry Problems
Key Points
To establish synthetic and vector proofs for two advanced problems in Euclidean geometry.
Developed synthetic proofs for mixtilinear incircles and incenter-circumcenter properties.
Constructed vector-based proofs to validate the findings.
Demonstrated new insights into the properties of mixtilinear incircles.
Confirmed the orthogonality between incenter and circumcenter using both proof methods.
Abstract
This article presents original synthetic and vector proofs for two advanced Euclidean geometry problems, establishing key properties of mixtilinear incircles and incenter-circumcenter orthogonality.