Let `A(5,-3), B (2,7) and C (-1, 2)` be the vertices of a `triangle ABC`. If P is a point inside the triangle ABC such that the triangle APC,APB and BPC have equal areas, then length of the line segment PB is:

Let A ( 1, 0 ) , B ( 6, 2 ) and C (( 3 ) /(2), 6 ) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas , then the length of the line segment PQ, where Q is the point ( - ( 7 ) /(6), - ( 1 ) /(3)) , is _________.

Let A ( 1, 0 ) , B ( 6, 2 ) and C (( 3 ) /(2), 6 ) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas , then the length of the line segment PQ, where Q is the point ( - ( 7 ) /(6), - ( 1 ) /(3)) , is _________.

Let A (0,2 ) , B ( 3, 0 ) , C ( 6, 4 ) be the vertices of triangle and P is a point inside the triangle such that area of triangle APB, BPC and CPA are equal. Equation of circle circumscribing Delta APB is :

Let A (0,2 ) , B ( 3, 0 ) , C ( 6, 4 ) be the vertices of triangle and P is a point inside the triangle such that area of triangle APB, BPC and CPA are equal. Equation of circle circumscribing Delta APB is :

Let A(5,6), B(-2,3) and C(6,-1) be the vertices of Delta ABC . Find the coordinates of the centroid of the triangle.

A (1, 4), B (3, 2) and C (7,5) are vertices of a triangle ABC. Find : the co-ordinates of the centroid of triangle ABC.

P is a point on the median AD of the triangle ABC.Prove that triangle APB = triangle APC.

A (-3, 4), B (3, -1) and C (-2, 4) are the vertices of a triangle ABC. Find the length of line segment AP, where point P lies inside BC, such that BP: PC = 2 : 3.

The vertices of triangle ABC are A (4, 4), B (6, 3), C (2, -1), then angle ABC is equal to