MathDB
Equal segments again

Source: Baltic Way 2014, Problem 12

November 11, 2014
geometrycircumcircletrapezoidsymmetrygeometric transformationreflectionparallelogram

Problem Statement

Triangle ABCABC is given. Let MM be the midpoint of the segment ABAB and TT be the midpoint of the arc BCBC not containing AA of the circumcircle of ABC.ABC. The point KK inside the triangle ABCABC is such that MATKMATK is an isosceles trapezoid with AT∥MK.AT\parallel MK. Show that AK=KC.AK = KC.
Back to ProblemsView on AoPS