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