In the adjoining figure, P is an interior point of `DeltaABC`. Then prove that :
`AB+BC+CA lt 2(PA + PB +PC)`

Let O be any point in the interior of DeltaABC , prove that : AB+BC+CA lt 2 (OA+OB+OC)

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

In DeltaABC, D is any point on side BC. Prove that AB+BC+CA gt 2AD

In the adjoining figure, ABC is a triangle and D is any point in its interior. Show that BD+DC lt AB +AC .

In the adjoining figure, D is the mid-point of side AB of Delta ABC and P be any point on side BC. If CQ ||PD , then prove that: area of Delta BPQ = (1)/(2) xx " area of " Delta ABC

In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect point O. Prove that : AB+BC+CD+DA lt 2(AC+BD)

In the adjoining figure, if AB = BC and BX =BY, then show that AX=CY

In the adjoining figure, DE || BC . Prove that area (DeltaACD) = " area " (DeltaABE)

In the following figure, ABC is an equilateral triangle and P is any point in AC, prove that : (i) BP gt PA (ii) BP gt PC