Find the locus of centres of circles which touch two intersecting line

1.	Find the locus of centres of circles which touch two intersecting lines.
Answer» let l1 and l2 be two intersecting lines which intersect at point P.\xa0Let O be the centre of circle which touches both l1 and l2 .In triangles OAP and OBP, we haveOA=OB (each equal to radius)\xa0PA=PB(tangents to a circle are equal)\xa0OP=OPso, by sss congruence criteria, we haveΔOAP congruent to ΔBPO

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