Question

Triangles PBC, QBC and RBC are three isosceles triangles on the same base BC. Show that P, Q and R are collinear.

Answer 1

Given: $\Delta PBC,\Delta QBC,\Delta RBC$, such that $PB=PC,QB=QC,RB=RC$

$\because \Delta PBC$ is isosceles

$\therefore PB=PC$

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’

$\therefore$ 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