Mathematics
The locus of the centers of all circles, which are tangents to the arms AB and BC of angle ABC is :
perpendicular bisector of arm AB
perpendicular bisector of arm BC
bisector of angle ABC
none of these
Locus
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Answer
From figure,
PD = PE (Radius of circle with center P)
P'F = P'G (Radius of circle with center P')
∴ The centers of circles are equidistant from the lines AB and BC.
We know that,
The locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines.
∴ The locus of the centers of all circles, which are tangents to the arms AB and BC of angle ABC is the bisector of angle ABC.
Hence, Option 3 is the correct option.
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