Final answer:
Angle BCO is 44 degrees since AC is the diameter of the circle, and by using the inscribed angle theorem and the property that angles at the center are twice the angles at the circumference.
Step-by-step explanation:
The student has asked to find the measure of angle BCO, where O is the centre of the circle, BAO is 68 degrees, and AC is the diameter of the circle. Since AC is a diameter, triangle ABC is a semicircle and angle BAC is a right angle (90 degrees) by the inscribed angle theorem. Knowing that angle BAO is 68 degrees, we can find angle BAC by calculating 90 - 68, which gives us 22 degrees for angle BAC. Since O is the center of the circle, angles at the center are twice the angles at the circumference. Therefore, to find angle BCO, we simply double the angle BAC, giving us 2 * 22 degrees, which is 44 degrees. So, angle BCO is 44 degrees.