2019 AMC 10A Problem 13

Let \triangle ABC be an isosceles triangle with BC = AC and \angle ACB = 40^{\circ}. Construct the circle with diameter \overline{BC}, and let D and E be the other intersection points of the circle with the sides \overline{AC} and \overline{AB}, respectively. Let F be the intersection of the diagonals of the quadrilateral BCDE. What is the degree measure of \angle BFC ?

\textbf{(A) } 90 \qquad\textbf{(B) } 100 \qquad\textbf{(C) } 105 \qquad\textbf{(D) } 110 \qquad\textbf{(E) } 120

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.