Geometry Problem 1458: Triangle, Incircles, Excircle, Area, Step-by-step Illustration

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 \(\dfrac{A_{1}}{A_{2}}=\dfrac{{A_{3}}^{2}}{{A_{4}}^{2}}\).


Static Diagram of problem 1458

Dynamic Geometry 1458: Triangle, Incircles, Excircle, Area, Step-by-step Illustration. Using GeoGebra


Poster of the problem 1458 using iPad Apps

Poster of Problem 1458, Triangle, Incircles, Excircle, Area, Step-by-step Illustration, GeoGebra, iPad

Classroom Resource:
Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

  • To explore (show / hide): click/tap a check box.
  • To stop/play the animation: click/tap the icon in the lower left corner.
  • To go to first step: click/tap the "Go to step 1" button.
  • To manipulate the interactive figure: click/tap and drag the blue points or figures.

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