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在矿区地面测量中,后方交会应用甚广,计算方法也较多,本文介绍一种先计算三角形的两个外接圆圆心连线的方位角,然后计算待求点坐标的方法。 图1中A、B、C为三个已知点,P点为待求点,作△ABP和△BCP的外接圆O_1和O_2,O_1和O_2分别为圆心,根据几何定理有O_1O_2⊥BP。我们只要求出O_1O_2的方位角,即可算出BP边的方位角及长度,最后按导线计算法求得P点的坐标。公式推导如下: 在图1中,根据圆周角定理有:
In the ground survey of the mining area, the rear intersection is widely used and there are many calculation methods. This paper introduces a method of calculating the azimuth of the connection of two circumscribed circles of the triangle first and then calculating the coordinates of the point to be found. In Fig. 1, A, B and C are three known points, point P is the point to be solved, and circumscribed circles O_1 and O_2 of △ ABP and △ BCP are center points of O_1 and O_2 respectively. According to the geometric theorem, there are O_1O_2⊥BP. As long as we find the azimuth of O_1O_2, we can calculate the BP side of the azimuth and length, and finally calculated by the method of calculating the coordinates of the P point. Formula derived as follows: In Figure 1, according to the circular angle theorem: