Distance of circumcentre from side|Distance of incentre from vertex| Length of median| Regular polygon

Distance of the orthocenter H from vertex B is

If distance of centroid of triangle ABC from vertex A is 6 cm them find the length of median through point, A.

The product of the distances of the incentre from the angular points of a triangleABC is

The distance of the incentre of the triangle ABC from A is

(i) Find the Distance of incenter from vertex (ii) Find the Length of tangent from Vertices to incircle

Find the distance between the circumcentre and the incentre of the DeltaABC.

Consider the following statements : 1. If n ge 3 and mge3 are distinct positive integers, then the sum of the exterior angles of a regular polygon of m sides is different from the sum of the exterior angles of a regular polygon of n sides. 2. Let m, n be integers such that m gt n ge 3 . Then the sum of the interior angles of a regular polygon of m sides is greater than the sum of the interior angles of a regular polygon of n sides, and their sum is (m+n)(pi)/(2) . Which of the above statements is/are correct?

(i) A regular polygon has 2016 sides and r is the radius of the circle circumscribing the polygon. Particles of equal mass are placed at 2015 vertices of the polygon. Find the distance of the centre of mass of the particle system from the centre of the polygon. (ii) In the last problem you have been asked to remove any one particle from the system so that the centre of mass of the remaining 2014 particles lies farthest from the geometrical centre of the polygon. Which particle will you remove ?