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Problem 6

Part of 2015 PAMO

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Cyclic implies parallelogram - 2015 PAMO Problem 6

Source: 2015 Pan-African Mathematics Olympiad Problem 6

8/26/2015
Let ABCDABCD be a quadrilateral (with non-perpendicular diagonals).
The perpendicular from AA to BCBC meets CDCD at KK. The perpendicular from AA to CDCD meets BCBC at LL. The perpendicular from CC to ABAB meets ADAD at MM. The perpendicular from CC to ADAD meets ABAB at NN.
1. Prove that KLKL is parallel to MNMN. 2. Prove that KLMNKLMN is a parallelogram if ABCDABCD is cyclic.
geometryparallelogramParallel Lines