On incircles in triangles and quadrangles
This paper discusses basic properties of incircles in triangles and quadrangles. In particular, it will be shown that (1) Let P be a point on the side BC of a triangle ABC and let r, r2, r3, be the inradii of the triangles ABC, ACP, ABP, respectively. Then 1/2 + 1/3 - 1/2r3 = 2/ha where ha is the al...
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oai:animorepository.dlsu.edu.ph:etd_bachelors-168172022-02-08T01:31:48Z On incircles in triangles and quadrangles Denoga, Gerald L. Sianghio, Michael H. This paper discusses basic properties of incircles in triangles and quadrangles. In particular, it will be shown that (1) Let P be a point on the side BC of a triangle ABC and let r, r2, r3, be the inradii of the triangles ABC, ACP, ABP, respectively. Then 1/2 + 1/3 - 1/2r3 = 2/ha where ha is the altitude of ABC from A. (2) Consider a triangle ABC and points P, Q on the line segment BC. If T is the external homothety center of the incircles of the subtriangles ABP and AQC, then T is also the external homothety center of the incircles of the subtriangles ABQ and APC. 1996-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/16304 Bachelor's Theses English Animo Repository Triangles Finite generalized quadrangles Geometry, Plane Circle |
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Triangles Finite generalized quadrangles Geometry, Plane Circle |
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Triangles Finite generalized quadrangles Geometry, Plane Circle Denoga, Gerald L. Sianghio, Michael H. On incircles in triangles and quadrangles |
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This paper discusses basic properties of incircles in triangles and quadrangles. In particular, it will be shown that (1) Let P be a point on the side BC of a triangle ABC and let r, r2, r3, be the inradii of the triangles ABC, ACP, ABP, respectively. Then 1/2 + 1/3 - 1/2r3 = 2/ha where ha is the altitude of ABC from A. (2) Consider a triangle ABC and points P, Q on the line segment BC. If T is the external homothety center of the incircles of the subtriangles ABP and AQC, then T is also the external homothety center of the incircles of the subtriangles ABQ and APC. |
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text |
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Denoga, Gerald L. Sianghio, Michael H. |
author_facet |
Denoga, Gerald L. Sianghio, Michael H. |
author_sort |
Denoga, Gerald L. |
title |
On incircles in triangles and quadrangles |
title_short |
On incircles in triangles and quadrangles |
title_full |
On incircles in triangles and quadrangles |
title_fullStr |
On incircles in triangles and quadrangles |
title_full_unstemmed |
On incircles in triangles and quadrangles |
title_sort |
on incircles in triangles and quadrangles |
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Animo Repository |
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1996 |
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https://animorepository.dlsu.edu.ph/etd_bachelors/16304 |
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