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Johny
Posts:
4
Registered:
12/10/04


how do i prove the following?
Posted:
Mar 13, 2004 12:30 AM


ABC is a given triangle. The center of the circle through A, B and C is O. Relative to O, the position vectors of A,B, C are vector a, vector b and vector c. If H is the point with position vector a + b + c, prove that Vector AH, Vector BH and Vector CH are perpendicular to Vector BC, Vector CA, Vector AB respectively. If AÃÂ, BÃÂ, CÃÂ are the midpoints of vector BC, vector CA, vector AB respectively, prove that Vector AAÃÂ, Vector BBÃÂ, and Vector CC are concurrent in G and find the position vector of G. Prove that O, G, H lie on a straight line.



