RMO 1992, question no. 4

ABCD is a quadrilateral and P , Q are mid-points of CD, AB respectively. Let AP , DQ meet
at X, and BP , CQ meet at Y . Prove that
area of ADX + area of BCY = area of quadrilateral PXQY 

  1. The number of ways in which three non-negative integers \( n_1, n_2, n_3 \) can be chosen such that \( n_1+n_2+n_3 = 10 \) is
    (A) 66 (B) 55 (C) \( 10^3 \) (D) \( \dfrac {10!}{3!2!1!} \)

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