Problem 156

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Problem 156: (2019 AMC 10a, 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 $\angle BFC ?$ $\textbf{(A) } 90 \qquad$ $\textbf{(B) } 100 \qquad$ $\textbf{(C) } 105 \qquad$ $\textbf{(D) } 110 \qquad$ $\textbf{(E) } 120$

Solution

Exercise 156: Solution

Let $\triangle ABC$ be isosceles with $BC=AC$ and $\angle ACB=60^\circ$. Construct the circle with diameter $\overline{BC}$, meeting $\overline{AC},\overline{AB}$ at $D,E$. Let $F$ be the intersection of the diagonals of $BCDE$. What is $\angle BFC$?

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