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SM and CL are parallel

Source: Romanian MO 2010 Grade 7

August 6, 2012
geometryrectangleratioangle bisectorgeometry proposed

Problem Statement

Let ABCDABCD be a rectangle of centre OO, such that ∠DAC=60∘\angle DAC=60^{\circ}. The angle bisector of ∠DAC\angle DAC meets DCDC at SS. Lines OSOS and ADAD meet at LL, and lines BLBL and ACAC meet at MM. Prove that lines SMSM and CLCL are parallel.
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