Let ω be a circle with center O and let A be a point outside ω. The tangents from A touch ω at points B, and C. Let D be the point at which the line AO intersects the circle such that O is between A and D. Denote by X the orthogonal projection of B onto CD, by Y the midpoint of the segment BX and by Z the second point of intersection of the line DY with ω. Prove that ZA and ZC are perpendicular to each other. geometryperpendicularTangentscircle