Let A B C be a triangle with D the midpoint of side A B, E the midpoint of side B C, and F the midpoint of side A C. Let k_{1} be the circle passing through points A, D, and F; let k_{2} be the circle passing through points B, E, and D; and let k_{3} be the circle passing through C, F, and E. Prove that circles k_{1}, k_{2}, and k_{3} intersect in a point.