РЕШЕНИЕ:
S∆ABK + S∆AKM = S∆ / 2 ⇒ S∆ABK = S∆ / 2 – S∆AKM
BK:KM=10:9 ⇒
S∆ABK =
10
S∆AKM
__9
S∆ / 2 – S∆AKM =
10
S∆AKM
__9
9S∆ – 18 S∆AKM = 20 S∆AKM
38 S∆AKM = 9S∆
S∆AKM = 9S∆ / 38
∆AKM ∞ ∆NKB
AM =
KM
BN
__BK
x =
9
BN
__10
BN = 10x / 9
∆ACP ∞ ∆NBP
AC =
PC
BN
__BP
2x__ =
PC
10x / 9
__BP
9 =
PC
5
__BP
S∆ABP =
BP
S∆APC
__PC
S∆ABP =
9
S∆APC
__5
S∆ABP + S∆APC = S∆ ⇒ S∆ABP = S∆ – S∆APC
S∆ – S∆APC =
9
S∆APC
______5
5 S∆ – 5 S∆APC = 9 S∆APC
20 S∆APC = 5 S∆
S∆APC = S∆ / 4
S KPCM = S∆APC – S∆AKM = S∆ / 4– 9S∆ / 38 =
1 S∆ / 76
S KPCM / S∆= 1 S∆ / 76 : S∆ = 1/76
Ответ: 1/76