In right angled DeltaABC, `/_C= 90^(@)` and D, E, F are three points on BC such that they divide BC in eaual parts (see the given figure). Prove that `8(AF^(2)+AD^(2))= 11AC^(2)+5AB^(2)`.

In the given figure, if AD bot BC , prove that AB^(2)+CD^(2)= BD^(2)+AC^(2)

D is a point on side BC of triangle ABC such that AD = AC (see the given figure). Show that AB gt AD.

ABCD is a rhombus. Prove that AB^(2)+BC^(2)+CD^(2)+DA^(2)= AC^(2)+BD^(2) .

The perpendicular from A on side BC of a DeltaABC intersects BC at D such that DB= 3CD (see the given figure). Prove that 2AB^(2)= 2AC^(2)+BC^(2) .

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see the given figure). Show that AD = AE.

D and E are points on the sides CA and CB respectively of a DeltaABC right angled at C. Prove that AE^(2)+BD^(2)= AB^(2)+DE^(2) .

In a right trianlge ABC right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that 9(AQ^(2)+BP^(2))= 13AB^(2) .

If A, B and C are three points on a line, and B lies between A and C (see figure), then prove that AB + BC = AC.

In triangleABC , AD, BE, CF are the medians. Prove that, 4(AD^(2)+BE^(2)+CF^(2))= 3(AB^(2)+BC^(2)+AC^(2)) .

In a right triangle ABC right angled at C, P and Q are points on sides AC and CB respectively which divide these sides in the ratio of 2 : 1. Prove that (i) 9 AQ^(2) = 9AC^(2) + 4BC^(2) (ii) 9BP^(2) = 9BC^(2) + 4AC^(2) (iii) 9 (AQ^(2) + BP^(2)) = 13 AB^(2)