MathDB

9

Part of 2013 National Olympiad First Round

Problems(1)

P09 [Geometry] - Turkish NMO 1st Round - 2013

Source:

4/16/2013
Let ABCABC be a triangle with ∣AB∣=18|AB|=18, ∣AC∣=24|AC|=24, and m(BAC^)=150∘m(\widehat{BAC}) = 150^\circ. Let DD, EE, FF be points on sides [AB][AB], [AC][AC], [BC][BC], respectively, such that ∣BD∣=6|BD|=6, ∣CE∣=8|CE|=8, and ∣CF∣=2∣BF∣|CF|=2|BF|. Let H1H_1, H2H_2, H3H_3 be the reflections of the orthocenter of triangle ABCABC over the points DD, EE, FF, respectively. What is the area of triangle H1H2H3H_1H_2H_3?
<spanclass=′latex−bold′>(A)</span> 70<spanclass=′latex−bold′>(B)</span> 72<spanclass=′latex−bold′>(C)</span> 84<spanclass=′latex−bold′>(D)</span> 96<spanclass=′latex−bold′>(E)</span> 108 <span class='latex-bold'>(A)</span>\ 70 \qquad<span class='latex-bold'>(B)</span>\ 72 \qquad<span class='latex-bold'>(C)</span>\ 84 \qquad<span class='latex-bold'>(D)</span>\ 96 \qquad<span class='latex-bold'>(E)</span>\ 108
geometrygeometric transformationreflectionhomothetytrigonometry