In[]:=
f1=y1+Sqrt[L1^2-(x-x1)^2]
Out[]=
2
L1
-
2
(x-x1)
+y1
In[]:=
Solve[(x-x2)^2+(f1-y2)^2==L2^2,x]//FullSimplify
Solve
:There may be values of the parameters for which some or all solutions are not valid.
Out[]=
x
1
2(
2
(x1-x2)
+
2
(y1-y2)
)

2
L2
(x1-x2)+
2
L1
(-x1+x2)+(x1+x2)(
2
(x1-x2)
+
2
(y1-y2)
)-
-((
2
(L1-L2)
-
2
(x1-x2)
-
2
(y1-y2)
)(
2
(L1+L2)
-
2
(x1-x2)
-
2
(y1-y2)
)
2
(y1-y2)
)
,x
1
2(
2
(x1-x2)
+
2
(y1-y2)
)

2
L2
(x1-x2)+
2
L1
(-x1+x2)+(x1+x2)(
2
(x1-x2)
+
2
(y1-y2)
)+
-((
2
(L1-L2)
-
2
(x1-x2)
-
2
(y1-y2)
)(
2
(L1+L2)
-
2
(x1-x2)
-
2
(y1-y2)
)
2
(y1-y2)
)
