MathDB

33

Part of 2012 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 2012 Problem - 33 {Geometry}

Source:

7/1/2012
Let ABCDA′B′C′D′ABCDA'B'C'D' be a rectangular prism with ∣AB∣=2∣BC∣|AB|=2|BC|. EE is a point on the edge [BB′][BB'] satisfying ∣EB′∣=6∣EB∣|EB'|=6|EB|. Let FF and F′F' be the feet of the perpendiculars from EE at △AEC\triangle AEC and △A′EC′\triangle A'EC', respectively. If m(FEF′^)=60∘m(\widehat{FEF'})=60^{\circ}, then ∣BC∣/∣BE∣=?|BC|/|BE| = ?
<spanclass=′latex−bold′>(A)</span> 53<spanclass=′latex−bold′>(B)</span> 152<spanclass=′latex−bold′>(C)</span> 3215<spanclass=′latex−bold′>(D)</span> 553<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ \sqrt\frac53 \qquad <span class='latex-bold'>(B)</span>\ \sqrt\frac{15}2 \qquad <span class='latex-bold'>(C)</span>\ \frac32\sqrt{15} \qquad <span class='latex-bold'>(D)</span>\ 5\sqrt\frac53 \qquad <span class='latex-bold'>(E)</span>\ \text{None}
geometry3D geometryprismrectangletrigonometry