Consider:
n = 10; % number of points
d = 7; % distance to match
P = 10*rand(n,2); % example point list
D = sqrt((P(:,1)-P(:,1).').^2 + (P(:,2)-P(:,2).').^2); % distance table from each point to all other points
m = tril(ones(n)); m(m==0) = NaN; % make a triangular mask
Derr = abs(D-d).*m; % calculate error
[Da Na] = min(Derr,[],2); % minimize
[~, Nb] = min(Da,[],1);
% these are the points with distance most closely matching the target
Pa = P(Na(Nb),:)
Pb = P(Nb,:)
% show the distance between Pa,Pb
sqrt((Pa(1)-Pb(1)).^2 + (Pa(2)-Pb(2)).^2)
