두 원이 주어졌을 때, 공통 내접선의 교점과 기울기를 구하는 방법 (프로그램)

아래는 TI-nspire 에서 작성된 프로그램입니다. 

Define common_itl()=
Prgm
:© Request basic data for 2 circles
:Request "{x1,y1,r1} List =",circle1,0
:Request "{x2,y2,r2} List =",circle2,0
:
:© Check data compatibility
:If (circle2[1]-circle1[1])^(2)+(circle2[2]-circle1[2])^(2)<(circle1[3]+circle2[3])^(2) Then
:  Disp "Too close"
:  Goto end
:EndIf
:
:newList(3)→circle3
:
:© Redefine vars to draw graph
:circle1[1]→circle1.x
:circle1[2]→circle1.y
:circle1[3]→circle1.r
:circle2[1]→circle2.x
:circle2[2]→circle2.y
:circle2[3]→circle2.r
:
:© Calculate Internally Dividing Point
:((circle1[3]*circle2[1]+circle2[3]*circle1[1])/(circle1[3]+circle2[3]))→idp.x
:((circle1[3]*circle2[2]+circle2[3]*circle1[2])/(circle1[3]+circle2[3]))→idp.y
:
:© Calculate Distances between IDP and the center of circles
:Local circle1.ratio,circle2.ratio
:((circle1[3])/(circle1[3]+circle2[3]))→circle1.ratio
:((circle2[3])/(circle1[3]+circle2[3]))→circle2.ratio
:
:√((circle2[1]-circle1[1])^(2)+(circle2[2]-circle1[2])^(2))→distance.c1c2
:distance.c1c2*circle1.ratio→distance.c1idp
:distance.c1c2*circle2.ratio→distance.c2idp
:
:√(distance.c1c2^(2)-(circle1[3]+circle2[3])^(2))→distance.citl
:distance.citl*circle1.ratio→circle3.r
:circle3.r→circle3[3]
:
:© Calculate Slope of Tangent Line
:tan(((circle2[2]-circle1[2])/(circle2[1]-circle1[1])))→t1
:tan(((circle3[3])/(circle1[3])))→t2
:
:tan(t1+t2+((π)/(2)))→idp.slope1
:tan(t1-t2+((π)/(2)))→idp.slope2
:
:Disp "circle1=",circle1," and circle2=",circle2
:Disp "Intersection point of Common_ITL=",{idp.x,idp.y}
:Disp "Slope of Common_ITL=",approx({idp.slope1,idp.slope2})
:c1_itp()
:
:Lbl end
:EndPrgm