% ex_4_5_68aGraphic.m
% Script file to create graphic for Prob. 4.5 #68a.

% plot semicircle
x = linspace(-4,4,100);
y = sqrt(16-x.^2);
plot(x,y);               

hold on;
grid on;
axis equal;  % force correct aspect ratio

% plot origin, point (1,sqrt(3)), and closest point on semicircle
plot([0 1 2],[0 sqrt(3) 2*sqrt(3)],'o','MarkerFaceColor','k','MarkerSize',8);

% plot radius through (1,sqrt(3))
plot([0 2],[0 2*sqrt(3)], 'color', 'red');

% annotate (1,sqrt(3))... use LaTeX to get a nice radical sign
text(1, sqrt(3)-.3, '$(1,\sqrt{3})$', 'Interpreter', 'Latex', 'FontSize', 12);

% add right angle marker
ep = .1;
plot(2+[-ep -ep*(1+sqrt(3)) -ep*sqrt(3)], 2*sqrt(3)+[-ep*sqrt(3) ep*(1-sqrt(3)) ep], 'k');

h = gcf;  % get a handle to the current figure
set(h, 'color', 'w');  % change background color of figure to white