Problem

Source: Problem 2 Geometry

Tags: geometry, trapezoid, symmetry, geometry unsolved



2-There is given a trapezoid $ ABCD$.We have the following properties:$ AD||BC,DA = DB = DC,\angle BCD = 72^\circ$. A point $ K$ is taken on $ BD$ such that $ AD = AK,K \neq D$.Let $ M$ be the midpoint of $ CD$.$ AM$ intersects $ BD$ at $ N$.PROVE $ BK = ND$.