Turkish NMO First Round - 2012 Problem - 33 {Geometry}
Source:
July 1, 2012
geometry3D geometryprismrectangletrigonometry
Problem Statement
Let ABCDA′B′C′D′ be a rectangular prism with ∣AB∣=2∣BC∣. E is a point on the edge [BB′] satisfying ∣EB′∣=6∣EB∣. Let F and F′ be the feet of the perpendiculars from E at △AEC and △A′EC′, respectively. If m(FEF′)=60∘, then ∣BC∣/∣BE∣=?<spanclass=′latex−bold′>(A)</span>35<spanclass=′latex−bold′>(B)</span>215<spanclass=′latex−bold′>(C)</span>2315<spanclass=′latex−bold′>(D)</span>535<spanclass=′latex−bold′>(E)</span>None