In a triangle ABC, the excircle E is tangent to the side BC at T (see the figure below). D and F are the incenters of triangles ABT and ATC. If A1, A2, A3, A4 are the areas of triangles BDT, TFC, BTE, and CTE, prove that \(\dfrac{A_{1}}{A_{2}}=\dfrac{{A_{3}}^{2}}{{A_{4}}^{2}}\).
This step-by-step interactive illustration was created with GeoGebra.
GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.
Geometry Problems
Open Problems
Visual Index
Ten problems: 1411-1420
All Problems
Triangle
Circle
Triangle Centers
Circle Tangent Line
Incenter, Incircle
Excenter, Excircle
Triangle Area
Dynamic Geometry
GeoGebra
HTML5 and Dynamic Geometry
iPad Apps
View or Post a solution