Exercițiul 333

E.333.

Bălănoiu Cristian (Facebook)
Răspuns | Soluție

Răspuns: 5136.\dfrac{5\sqrt{13}}{6}.

Soluție:

Fie AD⊥BC, OM⊥BC, ON⊥AD, ND=x.AD \perp BC,~ OM \perp BC,~ ON \perp AD,~ ND=x.
S=AD⋅BC2⇒AD=3⇒BD=4.S=\dfrac{AD \cdot BC}{2} \Rightarrow \boxed{AD=3} \Rightarrow \boxed{BD=4}.
△OBC\triangle OBC isoscel ⇒BM=3⇒MD=1.\Rightarrow \boxed{BM=3} \Rightarrow \boxed{MD=1}.
R2=32+x2=12+(3−x)2⇒x=1/6⇒R=5136.R^2 = 3^2+x^2 = 1^2+(3-x)^2 \Rightarrow \boxed{x=1/6} \Rightarrow \boxed{R=\dfrac{5\sqrt{13}}{6}}.