In a cyclic quadrilateral $ABCD$, if $\angle ADB + \angle BDC = 1$ right angle, then which three points are collinear?

$\angle ADB$ is the inscribed angle on $AB$ and $\angle BDC$ on $BC$; their sum being one right angle ($90^\circ$) means $\angle ADC$ subtends a diameter, so $AC$ passes through the centre $O$, making $A,O,C$ collinear.