Question

Fie A∈C(O, 10 cm) si dreapta MA tangenta la cerc. Calculati perimetrul triunghiului AOM daca:
a) MA=9 cm; b) m(∡AMO)=30°

Answer 1

a)Se,formeaza,un,Δdr.OAM
AO=10cm(ipoteza,=r)
MA=9cm
Cu,t.Pit.,aflam,ipotenuza,OM
OM²=AO²+AM²
OM²=100+81
OM²=181
OM=√181
Perim.ΔOAM=19+√181

b)m(∡AMO)=30°=>AO,este,cateta,opusa,∡30°=OM/2=>OM=20cm
Cu,t.Pit.,aflam,cealalta,cateta,AM
AM²=OM²-AO²
AM²=400-100
AM²=300
AM=√300
AM=10√3
Perim.ΔOAM=30+10√3=10(3+√3)