Please help if you can, thank you

Use circumcenter theorem to solve for the given values

Given the diagram below, michael writes, "segment ac is congruent to segment ac." which of the following reasons allow him to write this statement?

If a distance of 75 yds is measured back from the edge of the canyon and two angles are measured , find the distance across the canyon angle acb = 50° angle abc=100° a=75 yds what does c equal?