Question

Find the locus of centres of circles which touch two intersecting lines.

Answer 1

In $△YXO$ and $△ZXO$,

$\angle OYX=\angle OZX(=90)$

$XO=XO$ (common)

$OY=OZ=$radius

$△YOX\cong △ZOX$ (By SAS congruence)

$\therefore \angle YXO=\angle ZXO$

Therefore Locus of the centre is a straight line bisecting them between two intersecting lines.