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.