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Part of 2010 Philippine MO

Problems(1)

2010 Philippines MO P2

Source:

11/16/2015
On a cyclic quadrilateral ABCDABCD, there is a point PP on side ADAD such that the triangle CDPCDP and the quadrilateral ABCPABCP have equal perimeters and equal areas. Prove that two sides of ABCDABCD have equal lengths.
geometrycyclic quadrilateralperimeterPMO2010