<Cir-2023-746>, hint

Consider xy coordinate, and let P on r be (p,0), let Q (0,q), T(x,y)

Let centers of circles be O', O" and the angle made with x-axis by line O'YO" be X.

q-y=x/cosX(sinX+1), y=(p-x)/cosX(sinX+1).

Thus (q-y)/x=y/(p-x), x/p-y, x/p+y/q=1.