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13

Part of 2002 National Olympiad First Round

Problems(1)

P13 [Geometry] - Turkish NMO 1st Round - 2002

Source:

8/8/2014
Let ABCDABCD be a trapezoid such that AB∥CDAB \parallel CD, ∣BC∣+∣AD∣=7|BC|+|AD| = 7, ∣AB∣=9|AB| = 9 and ∣BC∣=14|BC| = 14. What is the ratio of the area of the triangle formed by CDCD, angle bisector of BCD^\widehat{BCD} and angle bisector of CDA^\widehat{CDA} over the area of the trapezoid?
<spanclass=′latex−bold′>a)</span> 914<spanclass=′latex−bold′>b)</span> 57<spanclass=′latex−bold′>c)</span> 2<spanclass=′latex−bold′>d)</span> 4969<spanclass=′latex−bold′>e)</span> 13 <span class='latex-bold'>a)</span>\ \dfrac{9}{14} \qquad<span class='latex-bold'>b)</span>\ \dfrac{5}{7} \qquad<span class='latex-bold'>c)</span>\ \sqrt 2 \qquad<span class='latex-bold'>d)</span>\ \dfrac{49}{69} \qquad<span class='latex-bold'>e)</span>\ \dfrac 13
geometrytrapezoidratioincenterinradiusalgebrapolynomial