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Part of 2003 Polish MO Finals

Problems(1)

Prove that SD = SM - Poland 2003 Third Round

Source:

11/1/2010
In an acute-angled triangle ABC,CDABC, CD is the altitude. A line through the midpoint MM of side ABAB meets the rays CACA and CBCB at KK and LL respectively such that CK=CL.CK = CL. Point SS is the circumcenter of the triangle CKL.CKL. Prove that SD=SM.SD = SM.
geometrycircumcirclegeometric transformationrotationhomothetytrapezoidsymmetry