The map shows three bus stations at points A, B, and C. A tour from station A to the zoo and the port and back to A is 10km long. A tour from station B to the park and the zoo and back to B is 12km long. A tour from station C to the port and back is 13km long. Also, a tour from the Zoo to the park and the port and back to the Zoo is 15km long. How long is the shortest tour from A to B to C and back to A?

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

f

step-by-step explanation:

f