Given: ΔPBC,ΔQBC,ΔRBC, such that PB=PC,QB=QC,RB=RC
∵ΔPBC is isosceles
∴PB=PC
Now the locus of a point equidistant from B and C is the perpendicular bisector of the line segment BC. Let us name it as ‘l’
∴ P lies on l ….(1)
Similarly Q lies on l and so does R lies on l. ……(2)
From (1) and (2), P,Q,R are collinear