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P29 [Geometry] - Turkish NMO 1st Round - 2002

Source:

August 11, 2014
geometryangle bisector

Problem Statement

In △ABC\triangle ABC, angle bisector ıf CAB^\widehat{CAB} meets BCBC at LL, angle bisector of ABC^\widehat{ABC} meets ACAC at NN. Lines ALAL and BNBN meet at OO. If ∣NL∣=3|NL| = \sqrt 3, what is∣ON∣+∣OL∣|ON| + |OL|?
<spanclass=′latex−bold′>a)</span> 33<spanclass=′latex−bold′>b)</span> 23<spanclass=′latex−bold′>c)</span> 2<spanclass=′latex−bold′>d)</span> 3<spanclass=′latex−bold′>e)</span> 5 <span class='latex-bold'>a)</span>\ 3\sqrt 3 \qquad<span class='latex-bold'>b)</span>\ 2\sqrt 3 \qquad<span class='latex-bold'>c)</span>\ 2 \qquad<span class='latex-bold'>d)</span>\ 3 \qquad<span class='latex-bold'>e)</span>\ 5
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