!set title=Producto escalar y conjunto de puntos*
!if $wims_read_parm!=$empty
 !goto $wims_read_parm
!endif
oef2wims_version=3.22
language=fr
author=René Chaffard
email=chafrene@club-internet.fr
computeanswer=no
precision=1000
leftrange=-5.000000
rightrange=5.000000

ansorder=r,r,r
varcnt=62
prevarcnt=61
postvarcnt=0
replycnt=3
choicecnt=0
conditioncnt=0
feedbackcnt=1
format=html

val1=$imagedir
val2=$confparm1
val3=$confparm2
val4=$confparm3
val5=$confparm4

!if $testcondition=yes
 !goto test
!endif
!if $status=waiting
 !exit
!endif

tmp=!nonempty items $val2

tmp0=!randitem $tmp
val6=$(tmp0)

!ifval $val6 iswordof 1 2 3 4 5 
val6= $val6
!else
tmp0=!randint 1, 5

val6= $(tmp0)
!endif
tmp0=!randint 2, 8

val7=$[rint($(tmp0))]

!ifval $val6=2 
tmp0=!randint 2, 6

val7=$[rint( $(tmp0))]
!endif

!ifval $val6 = 5 
val8= un círculo de diámtero sobre \((AB))
!endif

!ifval $val6 <> 5 
val8= un círculo de centro distinto de \(I)
!endif
val9=-$val7-2,$val7+2
val10=-$val7-2,$val7+2
tmp=!nonempty items 0,20,30,60,90,120

tmp0=!randitem $tmp
val11=$(tmp0)
val12=animate 25,0.2,0	xrange $val10	yrange $val9	rotate $val11	text black, -$val7/2,0,medium, A	text black, $val7/2, 0,medium, B	line $(val10[1]),0,$(val10[2]),0,black	linewidth 2	line -$val7/2,0,$val7/2,0,blue	disk -$val7/2,0,5,blue	disk $val7/2,0,5,blue	linewidth 1	
val13=el conjunto vacío,una recta perpendicular a \((AB)),una recta paralela a (AB),un círculo de centro \( I),un único punto \( I),$val8
!if $val6=1 
tmp0=!randint -4, 4

val14=$[rint($(tmp0))]
val15=2
tmp=!translate ";': to $     $ in $val14/($val7^2)

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val16=$(tmp0)
val17=$val16
val18=reply1	reply2
val19=\(\special{color=green} \vec{AM} \cdot \vec{AB} = $val14 )
val20=$(val9[1])+s*($(val9[2])-$(val9[1]))
val12=$val12	 line $val16*$val7-$val7/2,$(val9[1]),$val16*$val7-$val7/2,$(val9[2]), green	 text red, $val16*$val7-$val7/2,$val20, medium, M	 dline -$val7/2,0,$val16*$val7-$val7/2,$val20,red 	 
!endif
!if $val6=2 
tmp0=!randint -6, 6

val14=$[rint($(tmp0))]
val21=$[rint((4*$val14+$val7^2))]

!ifval $val21>0 
tmp=!translate ";': to $     $ in sqrt($val21)/2

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val22= $(tmp0)
!endif
val17=$val22
!if $val21>0 
val15=4
!else

!ifval $val21<0 
val15= 1 
!else
val15= 5
!endif
!endif
val18=reply 1

!ifval $val21>0 
val18= $val18	 reply 2
!endif
val19=\( \special{color=green}\vec{AM} \cdot \vec{BM} = $val14 )
val12=$val12	 trange 0,2*pi	 plot red, $val22*cos(t),$val22*sin(t)	 text red , $val22*cos(2*pi*s),$val22*sin(2*pi*s),medium,M	 dlines red, -$val7/2,0,$val22*cos(2*pi*s),$val22*sin(2*pi*s),$val7/2,0	
!endif
!if $val6=3 
tmp0=!randint 0, 20

val14=$[rint($(tmp0))]
val21=$[rint((2*$val14-$val7^2))]

!ifval $val21>0 
tmp=!translate ";': to $     $ in sqrt($val21)/2

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val22= $(tmp0)
!endif
val17=$val22
!if $val21>0 
val15=4
!else
!if $val21<0 
val15=1
!else
val15=5
!endif
!endif
val18=reply 1

!ifval $val21>0 
val18= $val18	 reply 2
!endif
val19=\( AM^2 + BM^2 = $val14 )
val12=$val12	 trange 0,2*pi	 plot red, $val22*cos(t),$val22*sin(t)	 text red , $val22*cos(2*pi*s),$val22*sin(2*pi*s),medium,M	 dlines red, -$val7/2,0,$val22*cos(2*pi*s),$val22*sin(2*pi*s),$val7/2,0	
!endif
!if $val6=4 
tmp0=!randint -4, 4

val14=$[rint($(tmp0))]
val15=2
tmp=!translate ";': to $     $ in ($val14+$val7^2)/(2*$val7^2)

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val17=$(tmp0)
val18=reply 1	reply 2
val19=\(AM^2 - BM^2 = $val14)
val20=$(val9[1])+s*($(val9[2])-$(val9[1]))
val12=$val12	 line $val17*$val7-$val7/2,$(val9[1]),$val17*$val7-$val7/2,$(val9[2]), green	 text red, $val17*$val7-$val7/2,$val20, medium, M	 dline -$val7/2,0,$val17*$val7-$val7/2,$val20,red 	 
!endif
!if $val6=5 
tmp0=!randint 2, 4

val14=$[rint($(tmp0))]
val15=6
tmp=!translate ";': to $     $ in $val14/($val14+1)

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val17=$(tmp0)
tmp=!translate ";': to $     $ in $val14/($val14-1)

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val23=$(tmp0)
val18=reply 1	reply 2, reply 3
val19=\( AM = $val14 BM )
val24=$[-$val7/2+$val17*$val7]
val25=$[-$val7/2+$val23*$val7]
val22=$[($val25-($val24))/2]
val26=$[($val24+$val25)/2]
val12=$val12	 trange 0,2*pi	 plot red, $val26+($val22*cos(t)),$val22*sin(t)	 text red , $val26+$val22*cos(2*pi*s),$val22*sin(2*pi*s),medium,M	 dlines red, -$val7/2,0,$val26+$val22*cos(2*pi*s),$val22*sin(2*pi*s),$val7/2,0	
!endif

!ifval $val6 =4 or $val6=1 
val27= \(k)
!endif

!ifval $val6 =2 or $val6=3 
val27= Rayon
!endif

!ifval $val6 =5
val27= \(k_1)
!endif
oefsteps=$val18 
nextstep=!nosubst $val18 
!readproc oef/steps.proc
replytype1=radio
replyname1=Nature
replygood1=$val15;$val13
replytype2=formal
replyname2=$val27
replygood2=$val17
replytype3=formal
replyname3=\( k_2 )
replygood3=$val23
question=__EXECUTED_1692754_EXERCISE__

!goto stat

!exit

:question
$()	Se consideran dos puntos 
!insmath A
$() y 
!insmath B
$() del plano tales que 
!insmath AB
$() = $val7. El punto medio de 
!insmath [AB]
$() lo denotaremos por 
!insmath I
$().	Determinar el conjunto de puntos 
!insmath M
$() tales que : 	<p style="text-align:center"><font color="green">$val19</font>.</p>	<br/>	 
!if $m_step=1 
$()Determinemos en primer lugar la naturaleza del conjunto buscado.	 Es	 <ul>	 <li>  
!read oef/embed.phtml reply1,1 
$()</li>	 <li>  
!read oef/embed.phtml reply1,2 
$()</li>	 <li>  
!read oef/embed.phtml reply1,3 
$()</li>	 <li>  
!read oef/embed.phtml reply1,4 
$()</li>	 <li>  
!read oef/embed.phtml reply1,5 
$()</li>	 <li>  
!read oef/embed.phtml reply1,6 
$()</li>	 </ul>	  
!endif
$()	 
!if $m_step=2 and $val6=1 
$()Sea 
!insmath H
$() el punto de intersección de la recta buscada con 
!insmath (AB)
$().<br/>	  Se tiene entonces  <p style="text-align:center">
!insmath  \vec{AH} = k \vec{AB} 
$()</p>	  Determinemos 
!insmath k
$().	  
!endif
$()	 
!if $m_step=2 and $m_n=2 and $val6=2 
$()Determinemos el radio 
!endif
$()	 
!if $m_step=2 and $val6=5 
$()El diámetro esá sobre 
!insmath (AB)
$(), denotaremos por 
!insmath H
$() y 
!insmath K
$() los extremos de ese diámetro.	 Se tiene entonces <p style="text-align:center"> 
!insmath  \vec{AH} = k_1 \vec{AB} 
$() et 
!insmath  \vec{AK} = k_2 \vec{AB} 
$().</p>	  Determinamos 
!insmath  k_1
$() et 
!insmath k_2 
$() oů 
!insmath  k_1 < k_2 
$().	  
!endif
$()	 
!if $m_step=2 and $val6=4 
$()Sea 
!insmath H
$() el punto de intersección de la recta buscada con 
!insmath (AB)
$().	 Se tiene entonces   <p style="text-align:center"> 
!insmath  \vec{AH} = k \vec{AB} 
$() .</p> 	  Determinamos 
!insmath k
$().	  
!endif
$()	 	 
!if $m_step=2 and $m_n=2 and $val6=3 
$()Determinamos el radio del círculo. 	  <i>Se podrá utilizar si es necesario la función (raíz cuadrada) sqrt, sqrt(2) = 
!insmath  \sqrt{2} 
$()</i> 
!endif
$()	
$()
!exit

:hint
$()
$()
!exit

:help
$()
$()
!exit

:solution
$()
$()
!exit

:feedback
!ifval 1=1
 <p>	<center> 
!read oef/draw.phtml 200,200 \
$val12 
$()</center>
$()
!endif

!exit

:test

!exit

:stat
vsavelist=6,7,12,19
embedcnt=6
