Problem: We are given two (intersecting) lines, say $L_1$ and $L_2$ (in $xy$ plane). And we are given a point, say $P$, not lying any on the lines. Construct the circles that pass through $P$ and touch the given lines.
It is clear that the centres of the circles lie on angle bisector of the lines. But I am not able to precisely locate the centre.
Please help. Thanks in advance!