P is any point inside the triangle ABC. Prove that : `angleBPC gt angleBAC`.

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 _________.

P is any point in the interior of a triangle ABC. Prove that : PA+PB lt AC +BC

P is any point in the interior of a triangle ABC. Prove that : PA+PB lt AC +BC

O is any point in the interior of a triangle ABC. Prove that : OB + OC lt AB + AC. _Q01.png" width="60%">

AD is a median of triangle ABC. Prove that : AB+AC gt 2AD

P is any point inside a parallelogram ABCD. Prove that : Area (DeltaAPB)+Area(DeltaCPD) =Area(DeltaAPD)+Area(DeltaBPC)

AD is a median of triangle ABC. Prove that : AB+BC+AC gt 2AD

P is a point inside the triangle ABC. Lines are drawn through P, parallel to the sides of the triangle.The three resulting triangles with the vertex at P have areas 4,9 and 49 sq . units. The area of the triangle ABC is -

Construct a triangle ABC, having given AB = 4.8 cm, AC = 4 cm and angleA=75^(@) , Find a point P (i) inside the triangle ABC, (ii) outside the triangle ABC equidistant from B and C, and at a distance of 1.2 cm from BC.