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点P在△ABC所在平面外一点,点O是点P在面ABC内的射影(如图).众所周知:(1)点O为△ABC外心的充要条件是:PA=PB=PC(2)点O为△ABC垂心的充要要件是:PA⊥BC,PB⊥AC,PC⊥BA(3)点O为△ABC内心的充要条件是:∠PAB=∠PAC,∠PBA=∠PBC,∠PCB=∠PCA自然的我们会问:点O为△ABC重心的充要条?
Point P is outside the plane where △ABC is located, and point O is the projection of point P within plane ABC (pictured). It is well-known that: (1) The necessary and sufficient condition for point O to be △ABC is: PA=PB=PC ( 2) Point O is a △ ABC pent up and the main requirement is: PA ⊥ BC, PB ⊥ AC, PC ⊥ BA (3) point O is △ ABC heart is a necessary and sufficient condition: ∠ PAB = ∠ PAC, ∠ PBA = ∠ PBC, ∠ PCB = ∠ PCA Naturally we will ask: Point O is the △ ABC center of gravity of the charge and demand?