From July 22 to July 24, 2010, the Technische Universit¨at M¨unchen, Germany,
hosted the eighth edition of the now well-established ADG workshop dedicated
to Automatic Deduction in Geometry. From the first edition, which was held
in Toulouse in 1996, to ADG 2010, a slow mutation has taken place. The workshop
that was formerly centered around computer algebra became a larger forum
where several communities could exchange new ideas coming from various domains,
such as computer algebra, logic, computer-assisted proof, combinatorial
geometry or even software development, but all focused on proof in geometry.

ADG 2010 was a fruitful meeting where 19 papers, from 22 submissions, were
selected for presentation after a review process involving at least two reviewers
per article. The set of presentations was completed by an invited talk given
by Robert Joan-Arinyo from the Universitat Polit`ecnica de Catalunya, Spain.
ADG 2010 was also an enjoyable meeting thanks to the rigorous and flawless
organization of the Munich team (see the Organizing Committee list).

After the meeting, a new call for papers was launched, accepting contributions
not necessarily related to a presentation at ADG 2010.

The present volume of the LNAI series is the result of this selection process,
which includes a new review process and discussions within the Program Committee.
It is composed of 13 papers which present original research reflecting
the current state of the art in this field. The following categorization proposes
a key to understanding the papers. But, obviously as with all categorizations, it
is rather arbitrary and it should not be taken strictly. Most papers can indeed
also be considered from a radically different point of view.

Three papers deal with incidence geometry using some kind of combinatoric
argument. Susanne Apel and J¨urgen Richter-Gerbert explore two ways to automatically
prove a geometric theorem by discovering cancellation patterns. Dominique
Michelucci studies incidence geometry leading to two papers: one deals
with an abstract notion of line and the other concerns human readable proofs in
geometry.

Three papers fall in the domain of computer algebra. Daniel Lichtblau studies
a problem related to the locus of the midpoint of a triangle in a corner, which
is a variant of the “penny in a corner” problem, by using numeric, formal and
graphical tools. Pavel Pech exposes a method to automatically prove theorems
related to inequalities in geometry. Yu Zou and Jingzhong Zhang propose a way
to generate readable proofs using the so-called Mass Point Method involving
barycentric calculations with real or complex masses.