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Problem 2 (2nd jbmo tst)

Source: 2nd TST for JBMO, Moldova

March 31, 2006
geometryrectangleprojective geometryangle bisectorgeometry proposed

Problem Statement

Let ABCDABCD be a rectangle and denote by MM and NN the midpoints of ADAD and BCBC respectively. The point PP is on (CD(CD such that D∈(CP)D\in (CP), and PMPM intersects ACAC in QQ. Prove that m(∠MNQ)=m(∠MNP)m(\angle{MNQ})=m(\angle{MNP}).
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