# Solution to length of the belt

hello everyone i am looking at following problem from this link

it is possible to say that everything is explained detailed but i did not understand some of them 1.what about number 7?how is here written 7 without explanation what does it mean?then why is here mentioned semicircles i am confused about it it is drawn simple two circles please help me to understand everything given in above mentioned task

-
[Meta: This is at least the second question you ask from that page. It looks like a pretty unreliable source.] I don't understand why they are talking about semi-circles. However, the number $7 = 13.5-6.5$ is motivated by applying Pythagoras to determine the length of the blue line. (we know the lengths of the hypotenuse and the short leg) – t.b. Jul 7 '11 at 9:15

The reason you don't understand some of it is that it's wrong :-) The length of the belt is not given by two semicircles and two tangents; the belt follows the larger circle for more than a semicircle and the smaller circle for less than a semicircle, and the sum of these two contributions is not the sum of the lengths of two semicircles. For the correct solution you need to add $$2(13.5-6.5)\alpha=2(13.5-6.5)\arccos(24/25)\approx4$$ to the given incorrect solution, where $\alpha$ is the angle by which the belt follows the larger circle beyond a semicircle on each side.