The Crazy Bugs

The spring is coming and so the bugs are ready for action!
Please inspect the diagram below.
The bugs are situated on corners of a square 10 inches on a side.
Believe it or not - the bugs on corners A and C are male, and the bugs on corners B and D are female.
Simultaneously all the bugs are starting to move in a pattern – male to female.
So the A crawls directly toward B, B toward C, C toward D and D toward A.
They crawl at the same constant rate and someone will correctly guess that they will describe logarithmic spirals which meet at the center of the square.
How far does each bug travel before they meet?
The problem can be solved without Calculus!

Publish your answer here - The Crazy Bugs Puzzle

Solved By: ljsense