# Adams' Circle and the Gergonne Point

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Let ABC be a triangle and let A'B'C' be the contact triangle, whose vertices are the points where the incircle intersects ABC. The lines AA', BB' and CC' meet at the point G, called the Gergonne point. Draw lines through G and parallel to the sides of the contact triangle. These lines meet the sides of ABC in six concyclic points: P, Q, R, S, T, and U; that circle is called the Adams circle of ABC. Also, the incenter I of ABC is the center of the Adams circle.

Contributed by: Jay Warendorff (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

## Permanent Citation