MathDB

13

Part of 2010 National Olympiad First Round

Problems(1)

Turkey NMO 2010 1st Round - P13 (Geometry)

Source:

7/26/2012
Let DD and EE be points on respectively [AB][AB] and [AC][AC] of △ABC\triangle ABC where ∣AB∣=∣AC∣|AB|=|AC|, m(BAC^)=40∘m(\widehat{BAC})=40^\circ. Let FF be a point on BCBC such that CC is between BB and FF. If ∣BE∣=∣CF∣|BE|=|CF|, ∣AD∣=∣AE∣|AD|=|AE|, and m(BEC^)=60∘m(\widehat{BEC})=60^\circ, then what is m(DFB^)m(\widehat{DFB}) ?
<spanclass=′latex−bold′>(A)</span> 45∘<spanclass=′latex−bold′>(B)</span> 40∘<spanclass=′latex−bold′>(C)</span> 35∘<spanclass=′latex−bold′>(D)</span> 30∘<spanclass=′latex−bold′>(E)</span> 25∘ <span class='latex-bold'>(A)</span>\ 45^\circ \qquad<span class='latex-bold'>(B)</span>\ 40^\circ \qquad<span class='latex-bold'>(C)</span>\ 35^\circ \qquad<span class='latex-bold'>(D)</span>\ 30^\circ \qquad<span class='latex-bold'>(E)</span>\ 25^\circ
geometrygeometric transformation