SOLUTION
Notice that line BA is a radius of the circle.
Since line BC is a tangen then the measure of angle ABC is:
[tex]m\angle ABC=90^{\circ}[/tex]
Using Triangle Angle-Sum Theorem, it follows:
[tex]m\angle ABC+m\angle BAC+m\angle BCA=180^{\circ}[/tex]
This gives:
[tex]90^{\circ}+57^{\circ}+m\angle BCA=180^{\circ}[/tex]
Solving the equation gives:
[tex]\begin{gathered} 147^{\circ}+m\angle BCA=180^{\circ} \\ m\angle BCA=180^{\circ}-147^{\circ} \\ m\angle BCA=33^{\circ} \end{gathered}[/tex]
Therefore the required answer is:
[tex]m\angle BCA=33^{\circ}[/tex]
