#### Rad HAZU, Matematičke znanosti, Vol. 22 (2018), 119-127.

### CURVES OF CENTROIDS, GERGONNE POINTS AND
SYMMEDIAN CENTERS IN TRIANGLE PENCILS IN ISOTROPIC PLANE

### Mirela Katić Žlepalo and Ema Jurkin

Department of Civil Engineering, Zagreb University of Applied Sciences, 10 000 Zagreb, Croatia

*e-mail:* `mkatic@tvz.hr`
Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, 10 000 Zagreb, Croatia

*e-mail:* `ema.jurkin@rgn.hr`

**Abstract.** In this paper we consider a triangle pencil in an isotropic
plane consisting of the triangles that have the same circumscribed circle.
We study the curves of centroids, Gergonne points and symmedian centers
for such pencils of triangles. We also study the curves of centroids,
Gergonne points and symmedian centers for tangential triangles of such a
triangle pencil.

**2010 Mathematics Subject Classification.**
51N25.

**Key words and phrases.** Isotropic plane, pencil of triangles, centroid, Gergonne point,
symmedian center.

**Full text (PDF)** (free access)
DOI: http://doi.org/10.21857/9e31lhnplm

**References:**

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CrossRef

- Z. Kolar-Begović, R. Kolar-Šuper, J. Beban-Brkić and V. Volenec,
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MathSciNet

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CrossRef

- G. Salmon, A Treatise of the Higher Plane Curves: Intended as a Sequel to a Treatise
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