Question

triunghiul ABC si punctul M apartine AB . Construim ME paralel cu AC. E apartine Bc si MF paralel cu BC. F apartine AC. daca BM supra MA= 3 supra 4. BC=21, AC=14, aflati perimetrul patrulaterului MECF
B) in triunghiul ABC consideram punctele D apartine BC, E apartine AC, astfel incat DE paralel cu AB
Calculati AC, daca D apartine BC , AE+AC=28, BC=12 , DB=9
AE daca B apartine CD    CB supra CD = 5 supra 8 si EC=16

Answer 1

A) Daca MF || BC si ME || AC atunci MECF este paralelogram cu ME=CF si MF=EC

BM/MA=3/4
3MA=4BM=4(AB-MA)=4AB-4MA
7MA=4AB=>
MA/AB=4/7=AF/AC
AC=14
=> AF=14*4/7=8
FC=14-8=6
ME=FC=6

AF/AC=MF/BC=6/14
BC=21
=> MF=12*6/14=9
Ec=MF=9

P MECF=6+6+9+9=30

B)AE+AC=28 => AE=28-AC
BC=12
DB=9
Avem:
BD/BC=AE/AC
9/12=(28-AC)/AC
3/4=28/AC-AC/AC=28/AC-1
3/4+1=28/AC
7/4=28/AC
AC=28*4/7=16

Daca CB/CD=5/8
CB/CD=AC/EC
5/8=(EC-EA)EC=EC/EC-EA/EC=1-EA/16
EA/16=1+5/8=13/8
EA=16*5:8=10