Question

Точки M , N , K , L расположены в данном порядке на окружности . Найдите а.) m ( дуга MN ) , если m (ML) =115 m(NL)=55 . б.) m (NK) , если ( MK ) =37 , m (NL) = 65 , m(ML)=85 в.) m (KL) , если m (MN) = 39 , m( MK) = 94 , m ( NL) = 122 . По подробнее решение . Заранее спасибо .​

Answer 1

Punctele M, N, K, L sunt situate în ordinea dată pe cerc. Aflați:

a) m(arc MN) dacă m(arc ML)=115°, m(arc NL)=55°

b) m(arc NK) dacă m(arc MK)=37°, m(arc NL)=65°, m(arc ML)=85°

c) m(arc KL) dacă m(arc MN)=39°, m(arc MK)=94°, m(arc NL)=122°

Soluție:

m(arc MN)+m(arc NK)+m(arc KL)+m(arc LM) = 360°

a)

m(arc ML) = m(arc MN)+m(arc NL)

m(arc MN) = m(arc ML)-m(arc NL) = 115°-55°

⇒ m(arc MN) = 60°

b)

m(arc MK) = m(arc MN)+m(arc NK)

m(arc NL) = m(arc NK)+m(arc KL)

⇒ m(arc MK)+m(arc NL)+m(arc LM) = m(arc MN)+m(arc NK) + m(arc NK)+m(arc KL) + m(arc ML) = [m(arc MN)+m(arc NK)+m(arc KL)+m(arc LM)] + m(arc NK)

37°+65°+85° = 360°+m(arc NK)

m(arc NK) = 360°-187°

⇒ m(arc NK) = 173°

c)

m(arc NK) = m(arc MK)-m(arc MN) = 94°-39° = 55°

m(arc KL) = m(arc NL)-m(arc NK) = 122°-55°

⇒ m(arc KL) = 67°