РЕШЕНИЕ:
S∆ABK + S∆AKM = S∆ / 2 ⇒ S∆ABK = S∆ / 2 – S∆AKM
BK:KM=5:6 ⇒
S∆ABK =
5
S∆AKM
__6
S∆ / 2 – S∆AKM =
5
S∆AKM
__6
3S∆ – 6 S∆AKM = 5 S∆AKM
11 S∆AKM = 3S∆
S∆AKM = 3S∆ / 11
∆AKM ∞ ∆NKB
AM =
KM
BN
__BK
x =
6
BN
__5
BN = 5x / 6
∆ACP ∞ ∆NBP
AC =
PC
BN
__BP
2x__ =
PC
5x / 6
__BP
12 =
PC
5
__BP
S∆ABP =
BP
S∆APC
__PC
S∆ABP =
5
S∆APC
__12
S∆ABP + S∆APC = S∆ ⇒ S∆ABP = S∆ – S∆APC
S∆ – S∆APC =
5
S∆APC
______12
12 S∆ – 12 S∆APC = 5 S∆APC
17 S∆APC = 12 S∆
S∆APC = 12 S∆ / 17
S KPCM = S∆APC – S∆AKM = 12 S∆ / 17 – 3S∆ / 11 =
81S∆ / 187
S∆BKP = S∆ / 2 – S KPCM = S∆ / 2 – 81S∆ / 187 = 25S∆ / 374
S∆BKP / S KPCM = 25S∆ / 374 : 81S∆ / 187 = 25/374 ∙ 187/81 = 25/162
Ответ: 25/162