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Triangles in Circles

Source: 2019 AMC 10A #13

February 8, 2019
AMCAMC 10AMC 10 A2019 AMC 10A2019 AMCgeometryTriangle

Problem Statement

Let ΔABC\Delta ABC be an isosceles triangle with BC=ACBC = AC and ∠ACB=40∘\angle ACB = 40^{\circ}. Contruct the circle with diameter BC‾\overline{BC}, and let DD and EE be the other intersection points of the circle with the sides AC‾\overline{AC} and AB‾\overline{AB}, respectively. Let FF be the intersection of the diagonals of the quadrilateral BCDEBCDE. What is the degree measure of ∠BFC?\angle BFC ?
<spanclass=′latex−bold′>(A)</span>90<spanclass=′latex−bold′>(B)</span>100<spanclass=′latex−bold′>(C)</span>105<spanclass=′latex−bold′>(D)</span>110<spanclass=′latex−bold′>(E)</span>120<span class='latex-bold'>(A) </span> 90 \qquad<span class='latex-bold'>(B) </span> 100 \qquad<span class='latex-bold'>(C) </span> 105 \qquad<span class='latex-bold'>(D) </span> 110 \qquad<span class='latex-bold'>(E) </span> 120
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