Nice little Mathematical Puzzle

OK, so here we have a puzzle devised by myself and a friend back when I was a young lad.... Ages ago then....... This is the gist.......

ABC is a right angled triangle
BC equals six inches
AD equals 2.3 inches
Angle BCA is bisected by CD, so ....
Angle BCD equals Y degrees and
Angle DCA equals Y degrees

Right, that's the easy bit.... The task is to find out the value of the distance BD... Easy-peasy isn't it, go on then give it a go and send me your results with all stages of working out as per your homework of yesteryear. No prizes, just a mention that you are a right clever dicky.

Off you go then and as per usual you can click the photo to enlarge if you think it will help