p0=[5 5]';	% Initial guess
p=fminsearch(@dist2ABC, p0);

A=[0 0]';
B=[3 0]';
C=[0 4]';
cosAPB=dot(A-p, B-p)/(norm(A-p)*norm(B-p));
cosBPC=dot(B-p, C-p)/(norm(B-p)*norm(C-p));
cosCPA=dot(C-p, A-p)/(norm(C-p)*norm(A-p));
fprintf('APB=%g degrees\n', acos(cosAPB)*180/pi);
fprintf('BPC=%g degrees\n', acos(cosBPC)*180/pi);
fprintf('CPA=%g degrees\n', acos(cosCPA)*180/pi);

% ====== Create the objective function surface
x=linspace(-1, 4, 51);
y=linspace(-1, 5, 51);
for i=1:length(x)
	for j=1:length(y);
		zz(j,i)=dist2ABC([x(i), y(j)]);
	end
end
% ====== Mesh & contour plot
subplot(121); h=meshc(x, y, zz); axis image; box on
xlabel('X'); ylabel('Y'); zlabel('Z');
set(h(1), 'faceAlpha', 0.1);	% Make the mesh transparent
axisLimit=axis;
line(p(1), p(2), axisLimit(5), 'marker', '.', 'color', 'r');
line([A(1), B(1), C(1), A(1)], [A(2), B(2), C(2), A(2)], axisLimit(5)*[1 1 1 1], 'color', 'r', 'linewidth', 2);
% ====== Detailed contour plot
subplot(122); contour(x, y, zz, 100); axis image
xlabel('X'); ylabel('Y'); zlabel('Z');
line([A(1), B(1), C(1), A(1)], [A(2), B(2), C(2), A(2)], 'color', 'r', 'linewidth', 2);
line(p(1), p(2), 'marker', '.', 'color', 'r', 'markerSize', 20);
line(A(1), A(2), 'marker', '.', 'color', 'k', 'markerSize', 20);
line(B(1), B(2), 'marker', '.', 'color', 'k', 'markerSize', 20);
line(C(1), C(2), 'marker', '.', 'color', 'k', 'markerSize', 20);
text(A(1), A(2), 'A  ', 'horizon', 'right');
text(B(1), B(2), '  B');
text(C(1), C(2), 'C  ', 'horizon', 'right');
text(p(1), p(2), '  P');