Geometric algebraic approach to theorem proving in classical geometry has the advantage of nice geometric interpretations for its sufficiently short algebraic expressions, and hence is beneficial for extending geometric theorems beyond their original configurations, and may be more suitable for current LLM-based geometric reasoning. This talk first showcases the power of Null Geometric Algebra in efficiently extending classical geometric theorems by reducing the number of constraints in the geometric configurations, then discloses the intrinsic properties of Null Geometric Algebra supporting the efficiency, from both the algebraic and the geometric perspectives.