Reactive controllers for autonomous racing avoid the computational overhead of full ee-Think-Act autonomy stacks by directly mapping sensor input to control actions, eliminating the need for localization and planning. A widely used reactive strategy is FTG, which identifies gaps in LiDAR range measurements and steers toward a chosen one. While effective on fully bounded circuits, FTG fails in scenarios with incomplete boundaries and is prone to driving into dead-ends, known as FTG-traps. This work presents DTR, a reactive controller that combines Delaunay triangulation, from raw LiDAR readings, with track boundary segmentation to extract a centerline while systematically avoiding FTG-traps. Compared to FTG, the proposed method achieves lap times that are 70\% faster and approaches the performance of map-dependent methods. With a latency of 8.95 ms and CPU usage of only 38.85\% on the robot's OBC, DTR is real-time capable and has been successfully deployed and evaluated in field experiments.