A multi-lip drilling tool is described, in which main cutting edge transitions in the region of the drill into a center lip section, wherein a cooling duct that leads to the drill tip is formed in each drill web. The invention minimizes tensile stress spikes in the chip flute base, while at the same time ensuring that a hitherto unachievable coolant/lubricant quantity gets to the engaged main blade. This is ensured by selecting a duct cross sectional form similar to an unsymmetrical kidney, in which it is ensured the selected radii of curvature for the individual boundary curve sections causes as much coolant/lubricant as possible to arrive at the blade or in proximity thereto in the fastest way via the point thinning and its edges intersecting with drill core.