Question

Pls exercitile 7 si 8

Answer 1

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