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 P is any point in the interior of a parallelogram A B C D , then prove that area of the triangle A P B is less than half the area of parallelogram.

If (a,b),(x,y),(p,q) are the coordinates of circumcentre,centroid,orthocentre of the triangle then

If the vertices P,Q,R of a triangle PQR are rational points,which of the following points of thetriangle PQR is/are always rational point(s) ?(A) centroid(B) incentre(C) circumcentre(D) orthocentreAgrawn Korouteden36

If the centroid of the triangle formed by points P(a,b),Q(b,c) and R(c,a) is at the origin, what is the value of a+b+c?

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

Let A-=(6,7),B-=(2,3)a n dC-=(-2,1) be the vertices of a triangle. Find the point P in the interior of the triangle such that P B C is an equilateral triangle.

p : If a triangle is equilateral then its centroid, circumcenter and incentre lies at same point Converse of statement p is

In Figure, P is a point in the interior of a parallelogram A B C D . Show that a r( A P B)+a r( P C D)=1/2a r(^(gm)A B C D) a R(A P D)+a r( P B C)=a r( A P B)+a r( P C D)