Given a triangle ABC with the incircle I. Let E_{A}, E_{B}, E_{C}
be the excircles and T_{A}, T_{B}, T_{C} be the extouch points. The Lines AT_{A}, BT_{B}, CT_{C} concur in the Nagel point N and cuts the
incircle at I_{A}, I_{B}, I_{C}. Prove that AI_{A} = NT_{A},BI_{B} = NT_{B}, CI_{C} = NT_{C}.

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.

Geometry Problems

Open Problems

Visual Index

Ten problems: 1411-1420

All Problems

Triangle

Circle

Nagel Point

Triangle Centers

Circle Tangent Line

Incircle

Excircle

Dynamic Geometry

GeoGebra

HTML5 and Dynamic Geometry

iPad Apps

View or Post a solution