Let M be the intersection point of the medians AD and BE of a right triangle ABC (∠C=90∘),\linebreak ω1 and ω2 be the circumcircles of triangles AEM and CDM. It is known that the circles ω1 and ω2 are tangent. Find the ratio in which the circle ω1 divides AB.
Problem
Source: Kyiv mathematical festival 2018
Tags: Kyiv mathematical festival, geometry, tangent circles