arXiv subjects
Publications and source records attributed to Tran Quang Hung.
We establish some new generalizations of Erdős-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erdős-Mordell inequality. We also found two other variations of Erdős-Mordell inequality to be generalizable in the same way.
We establish two direct extensions to the Butterfly Theorem on the cyclic quadrilateral along with the proofs using the projective method and analytic geometry of the Cartesian coordinate system.
We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple extension of Morley's Theorem is created and proven.
We establish some new theorems on pentagon and pentagram.