I  was doing a qs......and i had to accumulate this info from quite diff places.....wasted quite a time........

 

so thought u guys won't have to........

 

 

 

CONCURRENCY FOR A POINT IN A TRIANGLE:

 

1.) CENTROID - The point of concurrency of medians of a triangle......

 

         FORMULA - x,y = (x₁ + x₂ + x₃)/3 similarly for y.

 

2 .) INCENTRE - the point of concurrency of angular bisectors...........

 

      FORMULA - x,y = (ax₁ + bx₂ +cx₃) / a+b+c.    similarly for y.

where a b and c are length of sides opposite in triangle ABC respectively...

 

3.) CIRCUMCENTRE - the point of intersection of perpendicular bisectors.....

 

          FORMULA - x,y = (x₁Sin 2A + x₂Sin 2B + x₃Sin 2C) / tan A + tanB + tanC

 

4.) ORTOCENTRE - the point of intersection of altitudes........

 

                FORMULA - x,y = (x₁ tanA + x₂ tanB + x₃ tanC) / tan A + tanB + tanC

 

NOTE - ITS ONLY FOR A CENTROID THAT ANSWER WILL DEPEND COMPLETELY ON COORDINATES OF VERTICES......