Geometry O.o

Genius CPhill strikes again! Thanks a million...you made it so much easier to understand! Now, I'll know how to do this in the future. Muchas Gracias, Senor CPhill! Lol ^_^ 

Angle CDO is a right angle, because a radius drawn to a tangent always meets that tangent at right angles.

And by the Pythagorean Theorem, OD^2 + CD^2  = CO^2

But, CO  = (BC + OB)   and OB = OD  because they are radii

So.......by substitution.....

OD^2  + CD^2  = CO^2

OD^2 + CD^2 = (BC + OD)^2

OD^2  + 30^2  = ( 13 + OD)^2      simplify

OD^2 + 900  = 169 + 26OD + OD^2     subtract OD^2  from both sides

900 = 169 + 26OD      subtract 169 from both sides

731  = 26OD   divide both sides by 26

731/ 26  = OD   = about 28.1

But OD is a radius ...... and the diameter is twice this   = 56.2 =  "B"

Thanks, CD.......that property of the radius meeting a tangent at right angles comes in handy, at times....!!!