  For a subset $A$ of $\{1,2,\ldots,N\}^2$ of size $\alpha N^2$ we show
existence of $(m,n)\neq(0,0)$ such that the set $A$ contains at least
$(\alpha^3 - o(1))N^2$ triples of points of the form $(a,b)$, $(a+m,b+n)$,
$(a-n,b+m)$. This answers a question by Ackelsberg, Bergelson, and Best from
arXiv:2101.02811. The same approach also establishes the corresponding result
for compact abelian groups. Furthermore, for a finite field $\mathbb{F}_q$ we
comment on exponential smallness of subsets of $(\mathbb{F}_q^n)^2$ that avoid
the aforementioned configuration. The proofs are minor modifications of the
existing proofs regarding three-term arithmetic progressions.
