Geometry Problem 1471: Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration

The figure below shows a point P inside (or outside) an equilateral triangle ABC. The points O1, O2, and O3 are the incenters of triangles APB, BPC and APC so that T1, T2, and T3 are tangency points. Prove that the lines T1O1, T2O2, and T3O3 are concurrent at a point D.


Static Diagram of Geometry Problem1471

Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration, iPad Apps


Poster of the Geometry Problem 1471 using iPad Apps

Poster Dynamic Geometry 1471: Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration Using GeoGebra, iPad Apps

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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