设P为三角形ABC内一点,若向量AP=2/5向量AB+1/5向量AC,则三角形ABP的面积与三角形BCP的面积比为:1/2
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![设P为三角形ABC内一点,若向量AP=2/5向量AB+1/5向量AC,则三角形ABP的面积与三角形BCP的面积比为:1/2](/uploads/image/z/1759814-62-4.jpg?t=%E8%AE%BEP%E4%B8%BA%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E5%86%85%E4%B8%80%E7%82%B9%2C%E8%8B%A5%E5%90%91%E9%87%8FAP%3D2%2F5%E5%90%91%E9%87%8FAB%2B1%2F5%E5%90%91%E9%87%8FAC%2C%E5%88%99%E4%B8%89%E8%A7%92%E5%BD%A2ABP%E7%9A%84%E9%9D%A2%E7%A7%AF%E4%B8%8E%E4%B8%89%E8%A7%92%E5%BD%A2BCP%E7%9A%84%E9%9D%A2%E7%A7%AF%E6%AF%94%E4%B8%BA%EF%BC%9A1%2F2)
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设P为三角形ABC内一点,若向量AP=2/5向量AB+1/5向量AC,则三角形ABP的面积与三角形BCP的面积比为:1/2
设P为三角形ABC内一点,若向量AP=2/5向量AB+1/5向量AC,则三角形ABP的面积与三角形BCP的面积比为:
1/2
设P为三角形ABC内一点,若向量AP=2/5向量AB+1/5向量AC,则三角形ABP的面积与三角形BCP的面积比为:1/2
AB上取E使AE=2/5AB,AC上取F使AF=1/5AC则AEPF是平行四边形,则PF/AB=2/5,再延长BP交AC于G,则GF/GA=PF/AB=2/5,所以GF=2/3AF=2/15AC,则AG=2/15AC+1/5AC=1/3AC,则AG/CG=1/2,所以ABP和BCP面积比=AG/CG=1/2
见图