Răspuns:
∆ABC≈∆AMN:MN ll BC
a) AM=14cm. AB=7cm AN=16cm
rapoarte de la asemănare
AM/AB=AN/AC=MN/BC
14/7=16/AC=MN/BC
AC=(7×16)/14=16/2=8cm
MB=AM-AB=14-7=7cm
NC=AN-AC=16-8=8cm
b)AM=9cm AB=3,2cm AC=8,4cm
AM/AB=AN/AC=MN/BC
9/3,2=AN/8,4
AN=(9×8,4)/3,2=9×2,1/0,8=189/8cm
NC=189/8-8,4=189/8-42/5=15,2cm
AN/AC=MN/BC
AC=8,4cm
MB=AM-AB=9-3,2=5,8cm
?MB=5,8,NC=15,2,AC=8,4cm
c)AM=8√7 AB=2√7 cmCN=12√2cm
?MB CA AN
MB=AM-AB=8√7-2√7=6√7cm
AM/AB=AN/AC
8√7/2√7=(12√7+AC)/AC
4AC=AC+12√7cm
3AC=12√7cm
AC=4√7cm
AN=4√7+12√7=16√7cm
