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Question

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

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Solution

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


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