Solving a single equation of two variables

I am new to maxima and am trying to solve the following relatively simple
equation for r:
    x = a * log(( a + sqrt( a^2 - r^2))/r) - sqrt(a^2 - r^2),

where x and r are variables and a is a constant.

I have tried a number of methods suggested on the mailing list this year
with no useful results.  Is this a due to a bug in Maxima or am I doing
something wrong?


An example session is below.


(C1) solve (x = a * log(( a + sqrt( a^2 - r^2))/r) - sqrt(a^2 - r^2),r);
							    2    2
2    2
						    SQRT(a  - r ) + a
x + SQRT(a  - r )
(D1) 					       [LOG(-----------------) =
-----------------]
							    r
a
(C2) simp (x = a * log(( a + sqrt( a^2 - r^2))/r) - sqrt(a^2 - r^2));
SIMP evaluates to TRUE
Improper name or value in functional position.
 -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);)
(C3) (C1) eval (x = a * log(( a + sqrt( a^2 - r^2))/r) - sqrt(a^2 - r^2));
				   2    2
			     SQRT(a  - r ) + a	        2    2
(D1) 	      EVAL(x = a LOG(-----------------) - SQRT(a  - r ))
				     r
(C2) eliminate (x = a * log(( a + sqrt( a^2 - r^2))/r) - sqrt(a^2 - r^2),
r);
THE ARGUMENTS MUST BOTH BE LISTS
 -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);)
(C3) (C1) eliminate (x = a * log(( a + sqrt( a^2 - r^2))/r) - sqrt(a^2 -
r^2), a);
THE ARGUMENTS MUST BOTH BE LISTS
 -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);)
(C2) (C1) x = a * log(( a + sqrt( a^2 - r^2))/r) - sqrt(a^2 - r^2);
				 2    2
			   SQRT(a  - r ) + a	      2	   2
(D1) 		 x = a LOG(-----------------) - SQRT(a  - r )
				   r
(C2) rat(%);
				 2    2
			   SQRT(a  - r ) + a	      2	   2
(D2)/R/ 	 x = a LOG(-----------------) - SQRT(a  - r )
				   r


Thanks for your help.

Best regards,
Herb
Herbert G. Desson, ACAS, MAAA

Actuary
JLT Risk Solutions
6 Crutched Friars
London EC3N 2PH

phone:  +44 (0)20 7528 4702
fax:       +44 (0)20 7558 3785




************************************************************
JLT Risk Solutions Ltd
6 Crutched Friars, London EC3N 2PH. Co Reg No 1536540
Tel: (44) (0)20 7528 4000   Fax: (44) (0)20 7528 4500
http://www.jltgroup.com
Lloyd's Broker.  Regulated by the General Insurance
Standards Council
------------------------------------------------------------
The content of this e-mail (including any attachments) as 
received may not be the same as sent. If you consider that 
the content is material to the formation or performance of 
a contract or you are otherwise relying upon its accuracy, 
you should consider requesting a copy be sent by facsimile 
or normal mail.  The information in this e-mail is 
confidential and may be legally privileged. If you are not 
the intended recipient, please notify the sender immediately 
and then delete this e-mail entirely - you must not retain, 
copy, distribute or use this e-mail for any purpose or 
disclose any of its content to others.

Opinions, conclusions and other information in this e-mail 
that do not relate to the official business of JLT Risk 
Solutions Ltd shall be understood as neither given nor 
endorsed by it.  Please note we intercept and monitor 
incoming / outgoing e-mail and therefore you should neither 
expect nor intend any e-mail to be private in nature.

We have checked this e-mail for viruses and other harmful 
components and believe but not guarantee it virus-free prior 
to leaving our computer system.  However, you should satisfy 
yourself that it is free from harmful components, as we do 
not accept responsibility for any loss or damage it may 
cause to your computer systems.
************************************************************