如图所示,在平行四边形ABCD中,已知AB=8,AD=5,∠DAB=60°,CP=3,则AP?BP的值是______

2025-05-18 16:15:07
推荐回答(1个)
回答(1):

CP
=3
PD

AP
=
AD
+
1
4
AB
BP
=
AD
?
3
4
AB

又∵AB=8,AD=5,
AP
?
BP
=(
AD
+
1
4
AB
)?(
AD
?
3
4
AB
)=
AD
2
-
1
2
AD
?
AB
-
3
16
AB
2
=25-
1
2
×8×5cos60°-
3
16
×82
=25-10-12=3.
故答案为3.