Answer: In order to solve this problem, you should use the Pythagorean theorem. Since FG is perpendicular to OP, and OP and OQ are radii of the same circle, then triangle OFG is a right triangle. Similarly, triangle ORS is also a right triangle. By using the Pythagorean theorem, you can find that:
OF = sqrt(OP^2 + FG^2) = sqrt(19^2 + 40^2) = sqrt(361 + 1600) = sqrt(1961)
and
OS = sqrt(OQ^2 + RS^2) = sqrt(19^2 + 37^2) = sqrt(361 + 1369) = sqrt(1740)
Therefore, the length of the segment connecting the feet of the altitudes is:
OF + OS = sqrt(1961) + sqrt(1740) = 27.2
So the answer is A. 27.2
Explanation: