If D is the midpoint of AC and C is the midpoint of Ab, then find the length of AB if AD=4cm.

In DeltaAEX, T is the midpoint of XE and P is the midpoint of ET. If DeltaAPE is equilateral of side length equal to unity, then the vaue of (AX)^(2) is _____

In squareABCD is a quadrilateral. M is the midpoint of diagonal AC and N is the midpoint of diagonal BD. Prove that : AB^(2)+BC^(2)+CD^(2)+DA^(2)=AC^(2)=AC^(2)+BD^(2)+4MN^(2).

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot

In Delta ABC , with angle B=90^(@) , BC=6 cm and AB=8 cm, D is a point on AC such that AD=2 cm and E is the midpoint of AB. Join D to E and extend it to meet at F. Find BF.

ABCD is quadrilateral such that all of its sides touch a circle . If AB = 6cm, BC = 6.5 cm and CD = 7cm , then find the length of AD .

(Apollonius theorem): If D is the midpoint of the side BC of a triangle ABC, then show by vector method that |vec(AB)|^(2) + |vec(AC)|^(2) = 2(|vec(AD)|^(2)+ |vec(BD)|^(2)).

D is the midpoint of the side BC of Delta ABC . If P and Q are points o AB and on AC such that DP bisects angle BDA and DQ bisects angle ADC , then prove that PQ || BC

In the triangle OAB , M is the midpoint of AB, C is a point on OM, such that 2 OC = CM . X is a point on the side OB such that OX = 2XB. The line XC is produced to meet OA in Y. Then (OY)/(YA)=