MathDB
KM _|_ AD, cyclic ABCD, BK=CK, <KBC+< AMB= 90^o

Source: IV Soros Olympiad 1997-98 R3 11.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 2, 2024
geometryperpendicular

Problem Statement

Let MM be the point of intersection of the diagonals of the inscribed quadrilateral ABCDABCD, and let the angle ∠AMB\angle AMB be an acute angle. On the side BCBC, as a base, an isosceles triangle BCKBCK is constructed in the direction external to the quadrilateral such that ∠KBC+∠AMB=90o\angle KBC+\angle AMB= 90^o. Prove that line KMKM is perpendicular to ADAD.
Back to ProblemsView on AoPS