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SM//CL wanted, ABCD rectangle , <DAC = 60^o

Source: 2011 Saudi Arabia Pre-TST November 2.4

December 31, 2021
geometryrectangleparallel

Problem Statement

Let ABCDABCD be a rectangle of center OO, such that ∠DAC=60o\angle DAC = 60^o. 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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