O is any point inside a rectangle ABCD (see Fig. 6.52). Prove that `OB^2 + OD^2 = OA^2 + OC^2`.

In Fig if AD bot BC , prove that AB^2 + CD^2 = BD^2 + AC^2 .

O is any point in the exterior of a DeltaABC . Prove that 2(OA + OB + OC) > (AB + BC + CA) .

O is any point in the exterior of a DeltaABC . Prove that 2(OA + OB + OC) > (AB + BC + CA) .

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AC^2+AB^2= 2AD^2+1/2BC^2 . .

The perpendicular from A on side BC of a Delta ABC intersects BC at D such that DB =3CD (see Fig) Prove that 2AB^2=2AC^2+BC^2

In the fig. the point O is in the inside of an equilateral quad. ABCD such that OB=OD. Prove that the points A,O and C are collinear

If P be any point in the plane of square ABCD, prove that PA^(2)+PC^(2)=PB^(2)+PD^(2)

O is any point in the interior of triangleABC such that OB=OC and AB=AC. Show that AO bisects angleA .

In the fig. prove that: AD+AB+BC+CD>2AC.

In fig., O is a point in the interior of a triangle ABC, OD bot BC, OE bot AC and OF bot AB. Show that:- OA^2+OB^2+OC^2-OD^2-OE^2-OF^2=AF^2+BD^2+CE^2 .