AB and CD are two mutually perpendicular diameters of a circle. Chord CB is extended beyond point B

AB and CD are two mutually perpendicular diameters of a circle. Chord CB is extended beyond point B to segment BE equal to CB. What are the mutual positions of the line DE and the circle?

Let point O be the center of the circle. Consider the triangle DCE: OB is the middle line, since B is the middle of the side CE (by condition), O is the middle of the diameter DC. The middle line is parallel to the base of DE, hence the angle of ODE is right. Thus, the line DE and OD are perpendicular. So DE is tangent to the circle and has one common point with it.