Circles with Centers at Vertices of Triangles in Barycentric Coordinates

In this paper, two types of circles related to a triangle in the Euclidean plane are studied: circles with a center at one vertex that pass through the midpoints of opposite sides, and circles with a center at one vertex that pass through the remaining vertices. The properties of these circles are studied and proved by using barycentric coordinates.

Authors

Institutions

Publication Details

Journal
Mathematics
Published
2026-04-01
DOI
https://doi.org/10.3390/math14071170
Primary Topic
Mathematics and Applications
Type
article
Field-Weighted Citation Impact
0.00

Funders

Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Circles with Centers at Vertices of Triangles in Barycentric Coordinates

Ema Jurkin, Marija Šimić Horvath, Vladimír Volenec
Mathematics
Mathematics and Applications
article

Circles with Centers at Vertices of Triangles in Barycentric Coordinates

Ema Jurkin, Marija Šimić Horvath, Vladimír Volenec
article en

Abstract

In this paper, two types of circles related to a triangle in the Euclidean plane are studied: circles with a center at one vertex that pass through the midpoints of opposite sides, and circles with a center at one vertex that pass through the remaining vertices. The properties of these circles are studied and proved by using barycentric coordinates.

MathematicsVol. 14(7)
University of Zagreb (HR)
European Commission
Openalex Percentile: Top 27%
Mathematics and Applications
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.