SINGLE FORMULA TO FIND COORDINATES OF CENTROID, CIRCUMCENTRE, ORTHOCENTRE, INCENTRE

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that vec O Pdot vec O Q+ vec O Rdot vec O S= vec O Rdot vec O P+ vec O Qdot vec O S= vec O Q . vec O R+ vec O Pdot vec O S Then the triangle PQ has S as its: circumcentre (b) orthocentre (c) incentre (d) centroid

The vertices of a triangle are A(-10, 8), B(14,8) and C(-10, 26) . Let G, I, H, O be the centroid, incentre, orthocentre, circumcentre respectively of Delta ABC .

Let P be a point interior to the acute triangle A B Cdot If P A+P B+P C is a null vector, then w.r.t traingel A B C , point P is its a. centroid b. orthocentre c. incentre d. circumcentre

Let P be a point interior to the acute triangle A B Cdot If P A+P B+P C is a null vector, then w.r.t traingel A B C , point P is its a. centroid b. orthocentre c. incentre d. circumcentre

Let P be a point interior to the acute triangle A B Cdot If P A+P B+P C is a null vector, then w.r.t traingel A B C , point P is its a. centroid b. orthocentre c. incentre d. circumcentre

If O is the circumcentre and P the orthocentre of Delta ABC , prove that vec(OA)+ vec(OB) + vec(OC) =vec(OP) .

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

Let the incentre of DeltaABC is I(2, 5). If A=(1, 13) and B=(-4, 1) , then the coordinates of C are

If the coordinates of orthocentre O' are centroid G of a DeltaABC are (0,1) and (2,3) respectively, then the coordinates of the circumcentre are

If the vertices of a triangle are at O(0, 0), A (a, 0) and B (0, b) . Then, the distance between its circumcentre and orthocentre is