Question

googoo

想請問這題詳解的第5個選項是怎麼推算出來的？因為有點看不太懂詳解，謝謝🙏

20
4811,在△ABC的三邊BC,CA,AB上分別取一點D、E、F,其中AD,BE,CF交於點P,
3
2
說明
若BP:PE = 2:1且AE:EC=3:7,則下列選項中的敘述哪些是正確的?
2
(1) AP
=
· AB + ½ ÃÈ AÌ = ½³ AB +½³½Ã¯
3
AP = - AB+ 3X SAC
5.
+
(2) AD
+
AD=
ABt
+
19
=
8
3 AC
•AB+-AC
8
(3) PA = PD PA²= - PD
PA=PD PPD
7
(4)AF:FB=5:7
忙_
CP = ½ + ½ CE = ½ C B + 1 CA - G≤t CB = c + CA
3
(5)△PAB面積:△PBC面積:APCA面積=3:57.
15 AP
15
S
,
=
(脑+戚)→15AP=SAō+3AC.225.7
-SAR - 3A6
18

11. (1) AP = 1 AB+ AE.
2k
(2) AD KAP
AP = ½- AB+ AE = AB+ AC
3
3
(2)石
k
板+等丽板+他
k
李+=====+
...D、B、C共線,
15
3
5
3.
AD AB+-AC.
88
(3) (2) AD=AP = PA=-PD.
(4) CP
2.
1-
7
7
CP = 1 CB+² ²CE = 1 CB + 1 - CA,
3 30 15
3
CF=1CP=
CF=tCP .CB+-
t
|+1
3
=-
=1⇒t=
7t
15
5
It CA,
15
5
,
4
7
x(0.J.D=M 21
HU CF = 12 CB + 11 CA
12
12
⇒ AF:FB=5:7.
=-
85-
3-
AP
8
+0
(5) (2) AP = -(-4B+-AC)
158
0-⇒-15 AP-5AB-3AC=0
⇒△PAB:△PBC:△PCA3+S
=[-31:15-5-3:-5=3:7:5.
ER
7 A
3
0-
E
F
141
1
P
7
B
2
C
D E
(0

Answer 1

Ian

如圖