# 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.

## Poster of the Geometry Problem 1471 using 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.

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.