Prove that the tangent at a to the circumcircle of triangle abc is parallel to bc where triangle abc is a isosceles triangle?

The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter, which is the point O, at which the perpendicular bisectors of the sides of the triangle are concurrent.

Since our triangle ABC is an isosceles triangle, the perpendicular line to the base BC of the triangle passes through the vertex A, so that OA (the part of the bisector perpendicular line to BC) is a radius of the circle O.

Since the tangent line at A is perpendicular to the radius OA, and the extension of OA is perpendicular to BC, then the given tangent line must be parallel to BC (because two or more lines are parallel if they are perpendicular to the same line).