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tangent construction using only ruler at given point

Source: 2010 XIII All-Ukrainian Tournament of Young Mathematicians, Qualifying p12

May 19, 2021
geometryconstructionRulertangentUkrainian TYM

Problem Statement

On the plane is drawn a triangle ABCABC and a circle ω\omega passing through the vertex CC, the midpoints of the sides ACAC and BCBC and the point of intersection of the medians of the triangle ABCABC. The point KK lies on the circle ω\omega such that ∠AKB=90o\angle AKB=90^o. Using only with a ruler, draw a tangent to the circle ω\omega at point KK.
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