Question

COROANĂ! !!

Paralelipipedul dreptunghic ABCDA'B'C'D' are AB=16 cm, BC=12 cm și CC'= 10 m. Calculați:

a) d (A';BC)
b) d (A';DC)
c) d (A'; BD)
d) d (A'; AC)
e) d (A; A'O)
f) d (A; (A'CD))

Answer 1

d( A', BC)=(T3p)=A'B=√(10²+16²)=2√89

d(A',DC) =(T3p)= A'D=√(10²+12²)=2√61

d(A', BD)=(T3p)= A'P, unde AP⊥BD, P∈BD
  AP= cat1*cat2/ip=AB *AD/BD=16*12/20=48/5
pt ca BD= √(16²+12²)=20
A'P=√(10²+(48/5)²)=....

d(AA', AC) =AA'=10

e) d (A; A'O) unde {O}=AC∩BD
AO =20:2=10
 
d (A; A'O)= AA'*AO/A'O= 10*10/10√2=5√2

f) d (A; (A'CD))
 (A'CD)≡identic ≡(A'B'CD)
 A'∈(A'AD),
(A'AD), ⊥(A'B'CD),
 (A'AD), ∩(A'B'CD)=A'D⇒d (A; (A'CD)) =d(A,A'D)=AA'*AD/A'D= 10*12/2√61=60/√61