Fie OM=bis. lui ∡AOB⇒ ∡AOM=∡MOB⇒m(∡AOB)=2m(∡AOM)
Fie ON=bis. lui ∡BOC⇒ ∡BON=∡NOC⇒m(∡BOC)=2m(∡BON)
∡AOB si ∡BOC= suplementare⇒
m(∡AOB) + m(∡BOC)=180
2m(∡AOM)+2m(∡BON)=180
2(m(∡AOM)+m(∡BON))=180
m(∡AOM)+m(∡BON)=180/2
m(∡AOM)+m(∡BON)=90⇒MO⊥ON
