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Turkish NMO First Round - 1999 P-21 (Geometry)

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July 3, 2012
geometrytrigonometrycircumcirclegeometric transformationreflectiontrapezoidangle bisector

Problem Statement

ABC ABC is a triangle with \angle BAC \equal{} 10{}^\circ, \angle ABC \equal{} 150{}^\circ. Let X X be a point on [AC] \left[AC\right] such that \left|AX\right| \equal{} \left|BC\right|. Find ∠BXC \angle BXC.
<spanclass=′latex−bold′>(A)</span> 15∘<spanclass=′latex−bold′>(B)</span> 20∘<spanclass=′latex−bold′>(C)</span> 25∘<spanclass=′latex−bold′>(D)</span> 30∘<spanclass=′latex−bold′>(E)</span> 35∘<span class='latex-bold'>(A)</span>\ 15^\circ \qquad<span class='latex-bold'>(B)</span>\ 20^\circ \qquad<span class='latex-bold'>(C)</span>\ 25^\circ \qquad<span class='latex-bold'>(D)</span>\ 30^\circ \qquad<span class='latex-bold'>(E)</span>\ 35^\circ
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