Causing a rotating arc to touch another curve and not intersect (collison detection problem)

I want to write a code where an arc stops rotating as soon as it comes in contact with a semi-circle.

I have written a code for the same but my arc dosent touch the circle but it slightly intersects it. Any way of modifying the code so that the arc will touch the semi-circle and not intersect it. I have put rotation of arc inside a while loop by using linspace for changing theta. But at place of touch the theta value exceeds than needed so as a result I get an intersection.

I used polyxpoly() for finding intersection. Condition for while loop is that as long as I have empty array loop continues but as soon as I get a value from polyxpoly() my loop stops.

clc,clear
R = 5;                     % radius of a circle
r = 10;                     % radius of arc
aa = 60*pi/180;              % arc angle
ap = 0*pi/180;             % arc position angle

% defining the semi-circle about the origin

t = linspace(0,pi);
[x,y] = pol2cart(t,R);      % circle data

% Shifting circle centre to (3.5,0)
x=x+3.5;
y=y+0;

% defining the arc about the origin
t1 = linspace(0,aa)-aa/2+ap;
[x1,y1] = pol2cart(t1,r); % arc data

% shifting arc-lower-end to (14,0)
delx=14-x1(1); % Finding the x difference between arc-lower-end x-coordinate & 14
dely=0-y1(1); % Finding the y difference between arc-lower-end y-coordinate & 0

x1=x1+delx;
y1=y1+dely;

theta =linspace(0,pi,1000);
i=1;
xc=[];
yc=[];

while isempty(xc)&& isempty(yc)

% create a matrix of these points, which will be useful in future calculations

v = [x1;y1];

% choose a point which will be the center of rotation

x_center = 14;

y_center = 0;

% create a matrix which will be used later in calculations

center = repmat([x_center; y_center], 1, length(x1));

% define a 60 degree counter-clockwise rotation matrix



R = [cos(theta(i)) -sin(theta(i)); sin(theta(i)) cos(theta(i))];

% do the rotation...

s = v - center;     % shift points in the plane so that the center of rotation is at the origin

so = R*s;           % apply the rotation about the origin

vo = so + center;   % shift again so the origin goes back to the desired center of rotation

% this can be done in one line as:

% vo = R*(v - center) + center

% pick out the vectors of rotated x- and y-data

x_rotated = vo(1,:);

y_rotated = vo(2,:);


[xc,yc] = polyxpoly(x_rotated,y_rotated,x,y)
[xc1,yc1] = polyxpoly(x1,y1,x,y)

i=i+1;
end


% make a plot
plot(x,y)
hold on 

plot(x1, y1, 'k-', x_rotated, y_rotated, 'r-', x_center, y_center, 'bo');

axis equal

Any suggestions are welcome