Originally Posted by

**Tonia99** Hello Earboth;

Thank you for taking the time to reply. Your answer for length “a” is correct but unfortunately I am still somewhat confused as to how you arrived at it. I understand your point 1, but am not sure what you mean (or why it is necessary) to invoke circles as mentioned in point 2.

**The trough-point is where 3 circles with centres at 3 of the field corners**

with radii 30, 40, 50 intersect

Pythagoras' theorem gives the equations of circles,

the set of all points at a fixed distance from the centre.

Also, if the length of one side of the field is “a”, then I would have thought that equation 2 in your list should be (a-x)^2 + y^2 = 40^2 and not (x-a)^2.

I was able to generate 4 simultaneous equations (see new diagram to accompany this).

Length of one side of field = A+B = C+D

A^2 + C^2 = 50^2

B^2 + C^2 = 40^2

B^2 + D^2 = 30^2

I am still unable to solve for A+B or for C+D. Any help or any additional details on Earboth’s solution would be greatly appreciated.

Thanks in advance to all who take the time to reply.

Kind regards,

Tonia