This is related to my previous problem: Relation between incentre of a triangle and a circle touching its two sides and circumcircle , where I have found an answer but stuck at the following fact.
Given two orthogonal circles ($c$ and $d$) draw a line passing through the centre of one circle $(O)$ and intersecting the other circle at points $A$ and $B$. Any circle passing through $A$ and $B$ is orthogonal to $\odot O$.
I believe this is a well-known property (not known to me). Is there any specific theorem which states this? Or do you have a proof?