Turkish NMO First Round - 2012 Problem - 29 {Geometry}
Source:
July 1, 2012
geometrytrigonometrytrig identitiesLaw of Sines
Problem Statement
Let D and E be points on [BC] and [AC] of acute △ABC, respectively. AD and BE meet at F. If ∣AF∣=∣CD∣=2∣BF∣=2∣CE∣, and Area(△ABF)=Area(△DEC), then Area(△AFC)/Area(△BFC)=?<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>22<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>1