Bµi tËp 1: Cho tø gi¸c låi ABCD cã
tæng hai ®êng chÐo b»ng d.
Chøng minh r»ng: S
8
2
d
≤
( S: diÖn tÝch tø gi¸c)
ACOB.
2
1
≤
Ta cã: S
(ABC)
ACOD.
2
1
≤
S = S
(ABC)
+ S
(ADC)
ACOBOD ).(
2
1
+≤
⇒
BDACS .
2
1
≤
( )
44
.
2
2
dBDAC
BDAC
=
+
≤
8
2
d
S
≤
=
⊥
BDAC
BDAC
Mµ
(C«si)
⇒
§¼ng thøc x¶y ra khi
A
O
B
C
D
Bµi tËp 3
!"
#$%&'!()*+!
,!-. /0
123
14/
5
≥
25
&
6
&
6
&
6
&
1&/
5#-7$
#8/
#$%2
19&3:661;</
/
!1
6
C¸ch 1:
=>?@A&!BC#6
!
9&
( ) ( )
2
.
4
1
.
2
1
.
2
1
CDABBDDCABBD
++≤+≤
19&
!@DE-#DFGHD!I?@AJ
E-K#A3L!#%H
16/
M#661;<
⇒
161N
A
D
B
C
O
C¸ch 2
!1
6
( ) ( )
DCABBDDCBDBDAB
+=+≤
.
2
1
2
1
M#661;<
⇒
61;<O
⇒
S
( )
BDBD
−≤
16.
2
1
!D9&
( )
BDBD
−≤
16.
2
1
⇔
&
O;<6<2
≤
0
Híng dÉn vÒ nhµ