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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Main Authors: Denoga, Gerald L., Sianghio, Michael H.
Format: text
Language:English
Published: Animo Repository 1996
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Online Access:https://animorepository.dlsu.edu.ph/etd_bachelors/16304
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Institution: De La Salle University
Language: English
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spelling 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
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
language English
topic Triangles
Finite generalized quadrangles
Geometry, Plane
Circle
spellingShingle Triangles
Finite generalized quadrangles
Geometry, Plane
Circle
Denoga, Gerald L.
Sianghio, Michael H.
On incircles in triangles and quadrangles
description 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.
format text
author 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
publisher Animo Repository
publishDate 1996
url https://animorepository.dlsu.edu.ph/etd_bachelors/16304
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