MathDB

6

Part of 2019 Czech-Polish-Slovak Junior Match

Problems(1)

cyclic ABCD and equal angles given, perpendicular wanted

Source: Czech-Polish-Slovak Match Junior 2019, team p6 CPSJ

1/20/2020
Given is a cyclic quadrilateral ABCDABCD. Points K,L,M,NK, L, M, N lying on sides AB,BC,CD,DAAB, BC, CD, DA, respectively, satisfy ∠ADK=∠BCK\angle ADK=\angle BCK, ∠BAL=∠CDL\angle BAL=\angle CDL, ∠CBM=∠DAM\angle CBM =\angle DAM, ∠DCN=∠ABN\angle DCN =\angle ABN. Prove that lines KMKM and LNLN are perpendicular.
cyclic quadrilateralperpendiculargeometry