A cone with base radius and vertical height both equal to 10 cm has been left on a horizontal table with its vertex pointing upwards by an absent-minded maths teacher.

Freddy the fly, who we have previously met in challenges 141, 147 and 163, lands on the cone at a point exactly 5 cm vertically above the table top. He then follows the shortest possible route across the curved surface of the cone to the point on the circumference of the base of the cone which is furthest from where he landed.

How long is Freddy’s route across the surface of the cone?