Question

fie a si b doua puncte pe un cerc de centru o astfel incat m(aôb)=a°. paralela prin a la ob intersecteaza a doua oara cercul in m, iar paralela prin b la oa intersecteaza a doua oara cercul in n. aflati masurile arcelor determinate de punctele m si n in cazurile: 1)a=50; 2)a=60.

Answer 1

m∡MAO=m∡AOB=m∡NBO=a° (alterme interne)

m∡MAO=m∡AMO (ΔAOM isoscel, OB si ON , raze)

m∡NBO=m∡ONB (ΔBON isoscel OB,ON raze)

atunci m∡MOA=m∡NOB=180-2a°

si m∡MON=2(180-2a°) +a°=360°-3a°=mas arc "mic" MN

iar mas arc mare MN= 360°-(360°-3a°)=3a°

pt cazurile particulare date

caz 1) 360-150=210° si celalalt150°

caz 2) 360-180=180° si celalat 180°

as elegant as that!!