The tangent of a circle always form 90 degree angle with the radius. So measure of angle ABO and angle ACO is 90 degrees each.
The sum of angles of a quadilateral is 360 degrees. So,
[tex]\angle BOC+\angle ABO+\angle ACO+\angle BAC=360[/tex]Substitute the measures of angles in the equation to obtain the measure of angle BOC.
[tex]\begin{gathered} \angle BOC+90+90+90=360 \\ \angle BOC=360-270 \\ =90 \end{gathered}[/tex]Thus, measure of angle BOC is 90 degrees.