# Geometry

## 1009 Submissions

[7] **viXra:1009.0046 [pdf]**
*submitted on 12 Sep 2010*

### Pantazi's Theorem Regarding the Bi-orthological Triangles

**Authors:** Ion Pătraşcu, Florentin Smarandache

**Comments:** 5 pages

In this article we'll present an elementary proof of a theorem of Alexandru Pantazi
(1896-1948), Romanian mathematician, regarding the bi-orthological triangles.

**Category:** Geometry

[6] **viXra:1009.0015 [pdf]**
*submitted on 13 Mar 2010*

### Smarandache's Concurrent Lines Theorem

**Authors:** M. Khoshnevisan

**Comments:**
2 pages.

In this paper we present the Smarandache's Concurrent Lines Theorem in the geometry
of the triangle.

**Category:** Geometry

[5] **viXra:1009.0013 [pdf]**
*submitted on 13 Mar 2010*

### Smarandache's Cevians Theorem (II)

**Authors:** M. Khoshnevisan

**Comments:**
2 pages.

In this paper we present the Smarandache's Cevians Theorem (II) in the geometry of the
triangle.

**Category:** Geometry

[4] **viXra:1009.0012 [pdf]**
*submitted on 13 Mar 2010*

### Smarandache's Cevians Theorem (I)

**Authors:** M. Khoshnevisan

**Comments:**
2 pages.

We present the Smarandache's Cevians Theorem in the geometry of the triangle.

**Category:** Geometry

[3] **viXra:1009.0011 [pdf]**
*submitted on 13 Mar 2010*

### Smarandache's Ratio Theorem

**Authors:** M. Khoshnevisan

**Comments:**
2 pages.

In this paper we present the Smarandache's Ratio Theorem in the geometry of the
triangle.

**Category:** Geometry

[2] **viXra:1009.0010 [pdf]**
*submitted on 13 Mar 2010*

### The Smarandache-Pătraşcu Theorem of Orthohomological Triangles

**Authors:** Mihai Dicu

**Comments:**
1 page.

The Smarandache-Pătraşcu Theorem of Orthohomological Triangles is the
folllowing:

**Category:** Geometry

[1] **viXra:1009.0006 [pdf]**
*replaced on 5 Sep 2010*

### Two Remarkable Ortho-Homological Triangles

**Authors:** Ion Pătraşcu, Florentin Smarandache

**Comments:**
11 pages

In a previous paper [5] we have introduced the ortho-homological triangles, which are
triangles that are orthological and homological simultaneously.
In this article we call attention to two remarkable ortho-homological triangles (the given
triangle ABC and its first Brocard's triangle), and using the Sondat's theorem relative to
orthological triangles, we emphasize on four important collinear points in the geometry of the
triangle. Orthological / homological / orthohomological triangles in the 2D-space are generalized
to orthological / homological / orthohomological polygons in 2D-space, and even more to
orthological / homological / orthohomological triangles, polygons, and polyhedrons in 3D-space.

**Category:** Geometry