РЕШЕНИЕ:
S∆ABK + S∆AKM = S∆ / 2 ⇒ S∆ABK = S∆ / 2 – S∆AKM
BK:KM=7:3 ⇒
S∆ABK =
7
S∆AKM
__3
S∆ / 2 – S∆AKM =
7
S∆AKM
__3
3S∆ – 6 S∆AKM = 14 S∆AKM
20 S∆AKM = 3S∆
S∆AKM = 3S∆ / 20
∆AKM ∞ ∆NKB
AM =
KM
BN
__BK
x =
3
BN
__7
BN = 7x / 3
∆ACP ∞ ∆NBP
AC =
PC
BN
__BP
2x__ =
PC
7x / 3
__BP
6 =
PC
7
__BP
S∆ABP =
BP
S∆APC
__PC
S∆ABP =
7
S∆APC
__6
S∆ABP + S∆APC = S∆ ⇒ S∆ABP = S∆ – S∆APC
S∆ – S∆APC =
7
S∆APC
______6
6 S∆ – 6 S∆APC = 7 S∆APC
13 S∆APC = 6 S∆
S∆APC = 6 S∆ / 13
S KPCM = S∆APC – S∆AKM = 6 S∆ / 13 – 3S∆ / 20 =
81S∆ / 260
S∆BKP = S∆ / 2 – S KPCM = S∆ / 2 – 81S∆ / 260 = 49 S∆ / 260
S∆BKP / S KPCM = 49 S∆ / 260 : 81S∆ / 260 = 49/260 ∙ 260/81 = 49/81
Ответ: 49/81