Let ABC and PQR be any two triangles in the same plane. Assume that the perpendiculars from the points A,B,C to the sides QR,RP,PQ respectively are concurrent. Using vector methods or otherwise, prove that the perpendiculars from P,Q,R to BC,CA,AB respectively are also concurrent.

Let ABC and PQR be any two triangles in the same plane. Assume that t

1.	Let ABC and PQR be any two triangles in the same plane. Assume that the perpendiculars from the points A,B,C to the sides QR,RP,PQ respectively are concurrent. Using vector methods or otherwise, prove that the perpendiculars from P,Q,R to BC,CA,AB respectively are also concurrent.
Answer» Let $A B C$ and $P Q R$ be any two triangles in the same plane. Assume that the perpendiculars from the points $A, B, C$ to the sides $Q R, R P, P Q$ respectively are concurrent. Using vector methods or otherwise, prove that the perpendiculars from $P, Q, R$ to $B C, C A, A B$ respectively are also concurrent.