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2021 Geo Div 1 P7

Source:

March 2, 2021
geometry

Problem Statement

Convex pentagon ABCDEABCDE has BC‾=17\overline{BC}=17, AB‾=2CD‾\overline{AB}=2\overline{CD}, and ∠E=90∘\angle E=90^\circ. Additionally, BD‾−CD‾=AC‾\overline{BD}-\overline{CD}=\overline{AC}, and BD‾+CD‾=25\overline{BD}+\overline{CD}=25. Let MM and NN be the midpoints of BCBC and ADAD respectively. Ray EAEA is extended out to point PP, and a line parallel to ADAD is drawn through PP, intersecting line EMEM at QQ. Let GG be the midpoint of AQAQ. Given that NN and GG lie on EMEM and PMPM respectively, and the perimeter of △QBC\triangle QBC is 4242, find the length of EM‾\overline{EM}.
Proposed by Adam Bertelli
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