Abstract: In order to solve the problem of gas extraction in coal mines, the " delta mode" layout method is used to shorten the interval between drainage holes, which effectively eliminates the blank zone of the gas, and at the same time brings the problems of increased number of boreholes and repeated drainage in some areas. Through theoretical calculation, the paper puts forward the design scheme of inscribed polygons in a circle and optimizes the best implementation scheme. At the same time, the optimization was performed in combination with the rock cross-cut uncovering example. The results show that compared with the traditional design of outburst prevention drilling, the engineering of the circle inscribed hexagon- when the effective extraction radius is R, the optimize drilling lay outing along the coal seam borehole distance of √3R, and lay outing inclination the coal seam borehole distance of 1.5R- is reduced by 3792m and the reduction rate is 23%, which has important theoretical significance and practical value.