% First part : solving constraints to obtain parameters values
syms a b c
% 3 equations with 3 unknowns :
eq1=(1+4*a-2)^2+(2-3*a-3)^2==(3*b-2)^2+(1+4*b-3)^2;%PA^2=PB^2
eq2=(1+4*a-2)^2+(2-3*a-3)^2==((3*c-2)^2+(1+4*c-3)^2;%PA^2=PC^2
eq3=(3*b-1)*(1+4*a-3*c)+(1+4*b-2)*((2-3*a)-(1+4*c))==0;%HB orth. to CA
[A,B,C]=solve([eq1,eq2,eq3],a,b,c)
%
% second part : plotting one of the results
clear all;close all;hold on;axis equal;grid on;
xAB=@(t)(3*t);yAB=@(t)(1+4*t);% param. equ. of line AB
T=0:0.1:1;plot(xAB(T),yAB(T),LS,'on');
xH=1;yH=2;plot(xH,yH,'*r');text(xH+0.1,yH,'H');
xP=2;yP=3;plot(xP,yP,'*r');text(xP-0.2,yP,'P');
m=4/25;p=(14+3*sqrt(6))/25;n=(14-3*sqrt(6))/25;%param. values obtain in the first part;
xA=@(a)(1+4*a);yA=@(a)(2-3*a);plot(xA(m),yA(m),'ob');text(xA(m),yA(m)-0.2,'A')
xB=@(b)(3*b);yB=@(b)(1+4*b);plot(xB(n),yB(n),'ob');text(xB(n)-0.3,yB(n)+0.1,'B')
xC=@(c)(3*c);yC=@(c)(1+4*c);plot(xC(p),yC(p),'ob');text(xC(p)+0.2,yC(p),'C')
plot([xC(p),xA(m),xB(n)],[yC(p),yA(m),yB(n)],LS,'on')