MathDB
P25 [Geometry] - Turkish NMO 1st Round - 2013

Source:

April 16, 2013
geometrycircumcircleangle bisector

Problem Statement

Let DD be a point on side [AB][AB] of triangle ABCABC with AB=AC|AB|=|AC| such that [CD][CD] is an angle bisector and m(ABC^)=40m(\widehat{ABC})=40^\circ. Let FF be a point on the extension of [AB][AB] after BB such that BC=AF|BC|=|AF|. Let EE be the midpoint of [CF][CF]. If GG is the intersection of lines EDED and ACAC, what is m(FBG^)m(\widehat{FBG})?
<spanclass=latexbold>(A)</span> 150<spanclass=latexbold>(B)</span> 135<spanclass=latexbold>(C)</span> 120<spanclass=latexbold>(D)</span> 105<spanclass=latexbold>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 150^\circ \qquad<span class='latex-bold'>(B)</span>\ 135^\circ \qquad<span class='latex-bold'>(C)</span>\ 120^\circ \qquad<span class='latex-bold'>(D)</span>\ 105^\circ \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}