# Dynamic Geometry 1473: Kosnita's Theorem, Triangle, Four Circumcenters,
Concurrent Line, Step-by-step Illustration

The
dynamic geometry figure below shows a triangle ABC with the circumcenter O. If O_{A}, O_{B}, and O_{C}, are the circumcenters of triangles BOC, AOC, and AOB, respectively, prove that lines AO_{A}, BO_{B}, and CO_{C} are concurrent.

See solution below

## Static Diagram of Geometry Problem 1473

## Poster of the Kornita's Theorem 1473 using iPad Apps

### Search gogeometry.com

###
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.

### Recent Additions

Geometry Problems

Open Problems

Visual Index

Ten problems: 1411-1420

All Problems

Triangle

Circle

Triangle Centers

Circumradius, Circumcenter

Concurrent lines

Classical Theorems

GeoGebra

HTML5 and Dynamic Geometry

iPad Apps

View or Post a solution