РЕШЕНИЕ:
S∆ABK + S∆AKM = S∆ / 2 ⇒ S∆ABK = S∆ / 2 – S∆AKM
BK:KM=4:9 ⇒
S∆ABK =
4
S∆AKM
__9
S∆ / 2 – S∆AKM =
4
S∆AKM
__9
9S∆ – 18 S∆AKM = 8 S∆AKM
26 S∆AKM = 9S∆
S∆AKM = 9S∆ / 26
∆AKM ∞ ∆NKB
AM =
KM
BN
__BK
x =
9
BN
__4
BN = 4x / 9
∆ACP ∞ ∆NBP
AC =
PC
BN
__BP
2x__ =
PC
4x / 9
__BP
9 =
PC
2
__BP
S∆ABP =
BP
S∆APC
__PC
S∆ABP =
2
S∆APC
__9
S∆ABP + S∆APC = S∆ ⇒ S∆ABP = S∆ – S∆APC
S∆ – S∆APC =
2
S∆APC
______9
9 S∆ – 9 S∆APC = 2 S∆APC
11 S∆APC = 9 S∆
S∆APC = 9 S∆ / 11
S KPCM = S∆APC – S∆AKM = 9 S∆ / 11 – 9S∆ / 26 =
135S∆ / 286
S∆AKM / S KPCM = 9S∆ / 26 : 135S∆ / 286 = 9/26 ∙ 286/135 = 11/15
Ответ: 11/15 
