If you draw a circle, locate the centre, then the inscribed triangle is isosceles.

Join the centre to all 3 triangle vertices.

The angle at A is now split into 2 equal 21 degree angles.

If we label the centre F, then angle FAB = angle FAC = 21 degrees.

The 3 triangles within the inscribed triangle ABC are all isosceles also.

Hence, angle FCA = angle FBA = 21 degrees.

The tangent is perpendicular to the line CF.

Therefore the sum of angles FCA and ACD is 90 degrees.

Hence angle ACD is 90-21 = 69 degrees.