How to construct a curve to replace the projected part of another curve?

In this image, there is a large bulge of the thin black line (data attached), how to construct a curve like the thick red line to replace the projected part and connect tangentially to two other parts of thin black line?

[Sam Chak]

As long as you can provide the tangents at the two contact points and the distance between them, it is entirely possible to construct a smooth, beautiful red curve.

Answer 1

[Matt J]

[x,y]=readvars('black thin line.xlsx');
[x,y]=splitapply( @(a,b)deal(mean(a),mean(b)), x,y,  findgroups(x) );

sub=~(24.7<=x & x<=26.5);
yf=interp1(x(sub),y(sub),x,'spline');

plot(x,y,'--',x,yf,'-'); 
axis square; axis padded

[wd w]

Matt J, thank you very much!