What must be true for a point to be a circumcenter

Josh has a rewards card for a movie theater he receives 15 points for becoming a rewards card holder he earns 3.5 points for each visit to the movie theater he needs at least 55 points to earn a free movie ticket which inequality can josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket.

The triangles in the diagram are congruent. if mzf = 40°, mza = 80°, and mzg = 60°, what is mzb?

F(x) = 1/x g(x)=x-4 can you evaluate (g*f)(0) ? why or why not?