Let P be a point on circumcircle of triangle ABC and perpendiculars PL PM and PN are drawn on the lines BC, CA and AB respectively prove that the point L, M, N are collinear
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Let S be the circumcentre of △ABC.
Let a,b,c and p be the orthocentre of vectors of A,B,C and P respectively with referentre to origin S.
SA=a,SB=b,SC=c,SP=p and ∣∣∣∣p∣∣∣∣=∣∣∣∣a∣∣∣∣=∣∣∣∣b∣∣∣∣=∣∣∣∣c∣∣∣∣=R=circumradius.
Now, a+b+
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