n=$teller
bewerking=bewerking4.proc
!if $graad=0
    R=$teller
!else
    R=$graad
!endif     
!if $taal=nl
    white=white
!else
    white=magenta
!endif
           
!if $R=1
    r=!randitem 2,3,4,5,6,7,8,9,10
    RR=$[$r^2]
    b=!randint $[-2*($r-1)],$[2*($r-1)]
    b=$[$b/2]
    f1=!rawmath sqrt($RR-x^2)
    f2=!rawmath -1*sqrt($RR-x^2)
    Y1=$b
    Y2=$b
    y1=$Y1
    y2=$Y2
    X1=sqrt($[$RR-($b)^2])
    X2=-sqrt($[$RR-($b)^2])
    !if $afrondingsfactor>0
        x1=$[(round($afrondingsfactor*$X1))/$afrondingsfactor]
	x2=$[(round($afrondingsfactor*$X2))/$afrondingsfactor]
    !else
    #test op sqrt(4)=2
	X1=sqrt($[$RR-($b)^2])
	X2=-sqrt($[$RR-($b)^2])
        test1=$[round(100000*($X1))/100000]
        test2=$[round(100000*($X2))/100000]
        !if $test1 = $[$X1]
	    X1=$test1
        !endif
        !if $test2 = $[$X2]
	    X2=$test2
    	!endif
	x1=$X1
	x2=$X2
    !endif
    coordinaat=($x1;$y1) en ($x2;$y1)
    punt=$X1,$Y1,$X2,$Y2
    GOED$n=$x1,$y1,$x2,$y2
    LATEX=\left\{ \begin{array}{c}x^2+y^2=$RR}\\\\g(x)=$b\end{array}\right.    
    !if $taal=nl
	nivo_title=Bepaal het snijpunt van<br>een cirkel en een rechte lijn
	somtekst$n=<p align="left">Bepaal het snijpunt van de gegeven cirkel en de horizontale lijn:</p>\
	<p align="left"><em>$AFRONDING</em></p>
	antwoord$n=Het goede antwoord is dus: $coordinaat
    !else
	nivo_title=Determine the intersection points of<br>a circle and a line.
	somtekst$n=<p align="left">Determine the intersection points of the circle and a straight line:</p>\
	<p align="left"><em>$AFRONDING</em></p>
	antwoord$n=The correct answer is: $coordinaat
    !endif	
    !if $wims_user=supervisor and $printbaar=0
	opgave$n=<textarea cols="30" rows="2" value="" name="ANT$n">$coordinaat</textarea>
    !else
    	opgave$n=<textarea cols="30" rows="2" value="" name="ANT$n"></textarea>
    !endif
    !if $PLAATJE=1    
	grafiek=hline 0,$b,green
    !endif
!endif

!if $R=2
    !if $afrondingsfactor=0
	afrondingsfactor=100
	!readproc $authordir/afronding.$taal
    !endif
    r=!randitem 2,3,4,5,6,7,8,9,10
    RR=$[$r^2]
    a=!randitem -5,-4,-3,-2,-1,1,2,3,4,5
    b=!randint $[-1*($r)],$r
    b=$[$b/2]
    !if $b!=0
	g=$a*x+$b
    !else
	g=$a*x
    !endif
    G=!texmath $g
    A=$[1+($a)^2]
    B=$[2*$a*$b]
    C=$[($b)^2-$RR]
    D=$[sqrt(($B)^2-4*$A*$C)]
    X1=$[(-1*$B+$D)/(2*$A)]
    X2=$[(-1*$B-$D)/(2*$A)]
    Y1=$[$a*$X1+$b]
    Y2=$[$a*$X2+$b]
    x1=$[(round($afrondingsfactor*$X1))/$afrondingsfactor]
    x2=$[(round($afrondingsfactor*$X2))/$afrondingsfactor]
    y1=$[(round($afrondingsfactor*$Y1))/$afrondingsfactor]
    y2=$[(round($afrondingsfactor*$Y2))/$afrondingsfactor]
    !if $afrondingsfactor>0
        x1=$[(round($afrondingsfactor*$X1))/$afrondingsfactor]
	x2=$[(round($afrondingsfactor*$X2))/$afrondingsfactor]
    !else
	#test op sqrt(4)=2
	X1=sqrt($[$RR-($b)^2])
	X2=-sqrt($[$RR-($b)^2])
        test1=$[round(100000*($X1))/100000]
        test2=$[round(100000*($X2))/100000]
        !if $test1 = $[$X1]
	    X1=$test1
        !endif
        !if $test2 = $[$X2]
	    X2=$test2
        !endif
	x1=$X1
	x2=$X2
	y1=$Y1
	y2=$Y2
    !endif
    punt=$X1,$Y1,$X2,$Y2
    GOED$n=$x1,$y1,$x2,$y2
    LATEX=\left\{ \begin{array}{c}x^2+y^2=$RR}\\\\g\left(x\right)=$G\end{array}\right.    
    !if $taal=nl
	coordinaat=($x1;$y1) en ($x2;$y2)
	somtekst$n=<p align="left">Bepaal het snijpunt van de gegeven cirkel en de rechte lijn:</p>\
	<p align="left"><em>$AFRONDING</em></p>
	nivo_title=Bepaal het snijpunt van <br>een cirkel en een rechte lijn
	antwoord$n=Het goede antwoord is dus: $coordinaat
    !else
	nivo_title=Determine the intersection points of<br>a circle and a line.
	coordinaat=($x1;$y1) and ($x2;$y2)
	somtekst$n=<p align="left">Determine the intersection points of the circle and the line:</p>\
	<p align="left"><em>$AFRONDING</em></p>
	antwoord$n=The correct answer is: $coordinaat
    !endif
    !if $wims_user=supervisor and $printbaar=0
	opgave$n=<textarea cols="30" rows="2" value="" name="ANT$n">$coordinaat</textarea>
    !else
	opgave$n=<textarea cols="30" rows="2" value="" name="ANT$n"></textarea>
    !endif
    !if $PLAATJE=1	
	grafiek=curve green,$g
    !endif
!endif

!if $R>2

    nivo_title=Determine the intersection of <br>a circle and a "root-function"
    !if $afrondingsfactor=0
	afrondingsfactor=100
	!readproc $authordir/afronding.$taal
    !endif
    a=!randitem -3,-2,-1,2,3
    !if $R=3
	r=!randitem 2,3,4,5,6,7,8,9,10
	b=!randint 1,$[$r-1]
    !else
	r=!randitem 5,6,7,8,9,10
	d=!randint 1,$r
	b=!randint $r,$[$r+$d]
    !endif
    RR=$[$r^2]	
    c=$[$a*$b]
    !if $a>0
	g=sqrt($a*x+$c)
	B=$a
	D=$[sqrt($a^2-4*($c-$RR))]
	!if $R=3 
	    X1=$[-0.5*$B+0.5*$D]
	    Y1=$[sqrt(($a)*$X1+$c)]
	!else
	    X1=$[-0.5*$B+0.5*$D]
	    Y1=$[sqrt(($a)*$X1+$c)]
	    X2=$[-0.5*$B-0.5*$D]
	    Y2=$[sqrt(($a)*$X2+$c)]
	!endif
    !else
	g=sqrt($a*x-$c)
	B=$a
	D=$[sqrt(($a)^2+4*($c+$RR))]
	!if $R=3
	    X1=$[-0.5*($B)-0.5*$D]
	    Y1=$[sqrt($a*$X1-$c)]
	!else
	    X1=$[-0.5*($B)-0.5*$D]	    
	    Y1=$[sqrt($a*$X1-$c)]
	    X2=$[-0.5*($B)+0.5*$D]	    
    	    Y2=$[sqrt($a*$X2-$c)]
	!endif
    !endif
    x1=$[round($afrondingsfactor*$X1)/$afrondingsfactor]
    y1=$[round($afrondingsfactor*$Y1)/$afrondingsfactor]
    x2=$[round($afrondingsfactor*$X2)/$afrondingsfactor]
    y2=$[round($afrondingsfactor*$Y2)/$afrondingsfactor]
    G=!texmath $g
    !if $R=3
	coordinaat=($x1;$y1) 
	GOED$n=$x1,$y1
	punt=$X1,$Y1
	snijpunt=het snijpunt
    !else
	coordinaat=($x1;$y1) en ($x2;$y2)
	GOED$n=$x1,$y1,$x2,$y2
	punt=$X1,$Y1,$X2,$Y2
	snijpunt=de snijpunten
    !endif
    LATEX=\left\{ \begin{array}{c}x^2+y^2=$RR}\\\\g\left(x\right)=$G\end{array}\right.    
    !if $taal=nl
        somtekst$n=<p align="left">Bepaal $snijpunt van de gegeven cirkel en de wortelfunctie:</p>\
	<p align="left"><em>$AFRONDING</em></p>
	antwoord$n=Het goede antwoord is dus: $coordinaat
    !else
        somtekst$n=<p align="left">Determine the intersection point(s) of circle and "root-function"</p>\
	<p align="left"><em>$AFRONDING</em></p>	
	antwoord$n=The correct answer is: $coordinaat
    !endif
    !if $wims_user=supervisor and $printbaar=0
	opgave$n=<textarea cols="30" rows="2" value="" name="ANT$n">$coordinaat</textarea>
    !else
	opgave$n=<textarea cols="30" rows="2" value="" name="ANT$n"></textarea>
    !endif
    !if $PLAATJE=1
	grafiek=plotstep 1000\
	curve green,$g	
    !endif
!endif
!if $PLAATJE=1
    XSIZE=300
    YSIZE=300
    XRANGE=-12,12
    YRANGE=-12,12
    XSCHAAL=2
    YSCHAAL=2
    !readproc $authordir/ruitjespapier.proc
    knipperen=1
    aantal_beeldjes=2
    plaatje$n=300,300\
	$ruitjespapier\
	transparent $white\
	xrange $XRANGE\
        yrange $YRANGE\
	linewidth 2\
	ellipse 0,0,$[2*$r],$[2*$r],red\
	$grafiek\
        linewidth 1\
        vline 0,0,blue\
        hline 0,0,blue\
	linewidth s*14\
	points green,$punt\
	text black,9,-0.5,normal,x-axis\
	textup black,-1,10,normal,y-axis
!endif  
    
hint=$empty

 
  
