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: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1996
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16304 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | 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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