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 triangle `A B C ,` point `P` is its a. centroid b. orthocentre c. incentre d. circumcentre

If in a triangle ABC, sin A, sin B, sin C are in A.P, then

D , E ,a n dF are the middle points of the sides of the triangle A B C , then (a) centroid of the triangle D E F is the same as that of A B C (b) orthocenter of the tirangle D E F is the circumcentre of A B C

P is the variable point on the circle with center at C. C A and C B are perpendiculars from C on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle P A B is a circle with center at the centroid of triangle C A B and radius equal to the one-third of the radius of the given circle.

Let P (a, b , c ) be any point in space , state the signs of a , b and c if P lies on octant OXY ' Z

Let P (a, b , c ) be any point in space , state the signs of a , b and c if P lies on octant OX 'YZ

Let P (a, b , c ) be any point in space , state the signs of a , b and c if P lies on octant OXYZ

Let a,b,c be the sides of triangle whose perimeter is p and area is A, then

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A B in D ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

Let P (a, b , c ) be any point in space , state the signs of a , b and c if P lies on octant OX ' Y ' Z

Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y^2=5 . Then find the locus of the orthocentre of the triangle P A B , where P is any point moving on the circle.