MathDB

2

Part of 2003 Poland - Second Round

Problems(1)

Cyclic Quadrilateral, bisectors, points lie on perpendicular line

Source: 54 Polish MO 2003 Second Round - First Day Problem 2

2/19/2018
The quadrilateral ABCDABCD is inscribed in the circle oo. Bisectors of angles DABDAB and ABCABC intersect at point PP, and bisectors of angles BCDBCD and CDACDA intersect in point QQ. Point MM is the center of this arc BCBC of the circle oo which does not contain points DD and AA. Point NN is the center of the arc DADA of the circle oo, which does not contain points BB and CC. Prove that the points PP and QQ lie on the line perpendicular to MNMN.
geometrycyclic quadrilateralPolandbisectorperpendiculargeometry unsolved