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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