- P是三角形ABC内一点,延长AP、BP、CP与对边相交,图中a、?
- S△PBC/S△ABC=PD/AD=d/(a+d),
同理S△PCA/S△ABC=d/(b+d),
S△PAB/S△ABC=d/(c+d),
三式相加得1=d[1/(a+d)+1/(b+d)+1/(c+d)],
a+b+c=43,d=3,
∴(3+a)(3+b)(3+c)=3[(3+b)(3+c)+(3+c)(3+a)+(3+a)(3+b)],
∴27+9(a+b+c)+3(ab+bc+ca)+abc
=3[27+6(a+b+c)+bc+ca+ab)],
∴abc=54+9*43=441.