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P29 [Geometry] - Turkish NMO 1st Round - 2001

Source:

April 23, 2014
geometrytrapezoidtrigonometrypower of a point

Problem Statement

Let ABCDABCD be a isosceles trapezoid such that AB∣∣CDAB || CD and all of its sides are tangent to a circle. [AD][AD] touches this circle at NN. NCNC and NBNB meet the circle again at KK and LL, respectively. What is ∣BN∣∣BL∣+∣CN∣∣CK∣\dfrac {|BN|}{|BL|} + \dfrac {|CN|}{|CK|}?
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 9<spanclass=′latex−bold′>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ 8 \qquad<span class='latex-bold'>(D)</span>\ 9 \qquad<span class='latex-bold'>(E)</span>\ 10
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