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25

Part of 1999 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 1999 P-25 (Geometry)

Source:

7/3/2012
\angle BAC \equal{} 80{}^\circ, \left|AB\right| \equal{} \left|AC\right|, K∈[AB] K\in \left[AB\right], L∈[AB L\in \left[AB\right., \left|AB\right|^{2} \equal{} \left|AK\right|\cdot \left|AL\right|, \left|BL\right| \equal{} \left|BC\right|, \angle KCB \equal{} ?
<spanclass=′latex−bold′>(A)</span> 20∘<spanclass=′latex−bold′>(B)</span> 25∘<spanclass=′latex−bold′>(C)</span> 30∘<spanclass=′latex−bold′>(D)</span> 35∘<spanclass=′latex−bold′>(E)</span> 40∘<span class='latex-bold'>(A)</span>\ 20^\circ \qquad<span class='latex-bold'>(B)</span>\ 25^\circ \qquad<span class='latex-bold'>(C)</span>\ 30^\circ \qquad<span class='latex-bold'>(D)</span>\ 35^\circ \qquad<span class='latex-bold'>(E)</span>\ 40^\circ
geometry