7)
a) Daca ∡AOB≡∡BOC≡∡COD si sunt unghiuri in jurul unui punct
=> m(∡AOB)+M(∡BOC+m(∡COD)=360° => m(∡AOB)=360°:3=120°
Notam m(∡BOD) cu x => m(∡AOD)=3x
Daca D∈int(∡AOB) => ∡AOD+∡BOD=∡AOB
=> 3x+x=120° <=> 4x=120° => x=30° => m(∡AOD)=3·3x=3·30°=90°
=> AO⊥OD.
b) Daca OE bisectoare ∡BOC =>m(∡BOE)=m(∡EOC)=120°:2=60°
=> m(∡DOE)=m(∡DOB)+m(∡BOE)=30°+60°=90°
=> OD⊥OE
