Ketinit();
Setparent(Cdyname()+"fig");
Setketcindyjs(["Sc=1.2","Nolabel=all","Color=[0,0,0,0.2]"]);
Addax(0);

Menseki(p1,p2,p3):=(
 regional(v1,v2,S1);
 v1=p2-p1;v2=p3-p1;
 S1=(|v1.x*v2.y-v1.y*v2.x|)/2;
 S1;
);

Slider("K1-L1-M1",[-4,-2],[5,-2]);
m=floor(L1.x)+5;Expr([0,5],"w3","m="+m);
Slider("K2-L2-M2",[-4,-2.4],[5,-2.4]);
n=floor(L2.x)+5;Expr([0,5],"e3","n="+n);

Putpoint("A",[1,4],[A.x,A.y]);
Putpoint("B",[-4,0],[B.x,B.y]);
Putpoint("C",[4,0],[C.x,C.y]);

Listplot("1",[A,B,C,A]);
Letter([A,"n","A",B,"sw","B",C,"se","C"]);
S1=Menseki(A,B,C); //println(S1);

//m=2;n=1;
Letter([0,5.6],"c","点D,E,Fは辺BC,CA,ABをそれぞれ"+text(m)+":"+text(n)+"に内分する点");

pD=(n*B+m*C)/(m+n);pE=(n*C+m*A)/(m+n);pF=(n*A+m*B)/(m+n);
Pointdata("1",[pD,pE,pF]);
Letter([pD,"s","D",pE,"ne","E",pF,"nw","F"]);
Listplot("AD",[A,pD]);Listplot("BE",[B,pE]);Listplot("CF",[C,pF]);

pP=Op(1,Intersectcrvs("sgAD","sgBE"));//println(pP);
pQ=Op(1,Intersectcrvs("sgBE","sgCF"));//println(pQ);
pR=Op(1,Intersectcrvs("sgCF","sgAD"));//println(pR);
//Pointdata("2",[pP,pQ,pR]);
Letter([pP,"n","P",pQ,"n","Q",pR,"ne","R"]);
S2=Menseki(pP,pQ,pR); // println(S2);

Listplot("PQR",[pP,pQ,pR,pP]);//
Shade("1",["sgPQR"],["Color=green"]);

Expr(A+[1.5,0.8],"n","S_1="+Sprintf(S1,3));
Expr((pP+pQ+pR)/3,"c","S_2="+Sprintf(S2,3));
HI=S1/S2;//△ABCと△PQRの面積比

Expr([-4,4],"e","HI="+Sprintf(HI,5));
tmp="\Delta\mathrm{ABC}/\Delta\mathrm{PQR}="+Sprintf(HI,5);
Expr([7,4],"c",tmp);

Figpdf();
Windispg();

Help("Slider");
//Help("Putpoint");