WOLFRAM|DEMONSTRATIONS PROJECT

Tangent to a Catenary

​
a
x
Any tangent to the catenary
y=acosh(x/a)
has the property
AB=OP=a
​
, where
BC
is the tangent to the catenary at
C
, and
ABC
​
is the semicircle with center
(x,y/2)
and radius
y/2
.