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AKNM and ABC have equal areas (IMO SL 1987-P21)

Source:

August 19, 2010
geometrycircumcircletrigonometryarea of a triangleIMO Shortlist

Problem Statement

In an acute-angled triangle ABCABC the interior bisector of angle AA meets BCBC at LL and meets the circumcircle of ABCABC again at NN. From LL perpendiculars are drawn to ABAB and ACAC, with feet KK and MM respectively. Prove that the quadrilateral AKNMAKNM and the triangle ABCABC have equal areas.(IMO Problem 2)
Proposed by Soviet Union.
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