Q. 14.5( 11 Votes )

Find the locus of point ℓ equidistant from three vertices and three sides of a triangle.

Answer :

The locus of point ℓ equidistant from three vertices is the circumcentre and three sides of a triangle is the incentre of the triangle.


Here, J is the incentre of the ∆LMN.


At first draw the angle bisectors of all the angles i.e, L , M and N.


LO, MP and NQ are the angle bisectors respectively.


Let LO, MP and NQ intersect at J,


J is the incentre.



Here, U is the circumcenter of the ∆RST.


At first , draw the perpendicular bisectors of the sides ST, RT and RS of the triangle.


Here, RC, SB and AT are the required perpendicular bisectors.


Lat them intersect at U


Hence, U is the circumcenter of the triangle.


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