size(200);
import olympiad;
import geometry_dev;
pair A,B,C,M;
pair []intersect;
A=origin; B=(0,6); C=(7,0);
M = (B+C)/2; dot(M);
intersect = intersectionpoints(circle(A,5),line(B,C));
draw(circle(A,5),gray);
dot(intersect);
draw(A--intersect[0]);draw(A--intersect[1]);
draw(A--B--C--A--M);