Model
Digital Document
Publisher
Florida Atlantic University
Description
This thesis explores several construction problems related to the incircle of
a triangle. Firstly, as a generalization of a theorem of D. W. Hansen, we find two
quadruples of quantities related to a triangle which have equal sums and equal
sums of squares. We also study the construction problems of triangles with
centroid on the incircle, and those with a specified cevian - a median, an angle
bisector, or an altitude- bisected by the incircle. Detailed analysis leads to designs of animation pictures using the dynamic software Geometer's Sketchpad.
a triangle. Firstly, as a generalization of a theorem of D. W. Hansen, we find two
quadruples of quantities related to a triangle which have equal sums and equal
sums of squares. We also study the construction problems of triangles with
centroid on the incircle, and those with a specified cevian - a median, an angle
bisector, or an altitude- bisected by the incircle. Detailed analysis leads to designs of animation pictures using the dynamic software Geometer's Sketchpad.
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