intersection point between line and circle and draw tangent at that intersection point

Hi, please find below code mentied.i am trying to estimate a circle area by drawing tangents on circle.I need to draw a line from a point(in or out of circle) and draw tangent at intersection point.If i have point inside circle how to draw a line and find where it touches the circle.

x1=5; y1=5; r = 10; t = 0 : .1 : 2*pi; x = r * cos(t) + x1; y = r * sin(t) + y1; hold on; plot(x, y);

cnt=0; for l=1:20

    x2=20;
    y2=10;
    %line
    x3=randint(1,1,[-15 15]);
    y3=randint(1,1,[-15 15]);
     v1=rand(1);
     v2=rand(1);
       syms s
     eq=((x3+s*v1)-5).^2+((y3+s*v2)-5).^2-r.^2;
     sval=solve(eq,s)
     ansv= vpa(subs(eq,sval))

    if(ansv==0)

        svale(l,:)=vpa(sval);

        line([x2,x3],[y2,y3])

        %pointvals(l,:,:)=

        cnt=cnt+1;
    end   
    hold off
end
Please help me

Thanks, Sita