  Large Language Models (LLMs) demonstrate ever-increasing abilities in
mathematical and algorithmic tasks, yet their geometric reasoning skills are
underexplored. We investigate LLMs' abilities in constructive geometric
problem-solving one of the most fundamental steps in the development of human
mathematical reasoning. Our work reveals notable challenges that the
state-of-the-art LLMs face in this domain despite many successes in similar
areas. LLMs exhibit biases in target variable selection and struggle with 2D
spatial relationships, often misrepresenting and hallucinating objects and
their placements. To this end, we introduce a framework that formulates an
LLMs-based multi-agents system that enhances their existing reasoning potential
by conducting an internal dialogue. This work underscores LLMs' current
limitations in geometric reasoning and improves geometric reasoning
capabilities through self-correction, collaboration, and diverse role
specializations.
