# Geometry Problem 1455: Nagel Point, Excircles, Incircle, Congruent Segments

Given a triangle ABC with the incircle I. Let EA, EB, EC be the excircles and TA, TB, TC be the extouch points. The Lines ATA, BTB, CTC concur in the Nagel point N and cuts the incircle at IA, IB, IC. Prove that AIA = NTA,BIB = NTB, CIC = NTC.

## Poster of the problem 1455 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.