ABC is a right triangle , right angled at A and D is the mid point of AB . Prove that `BC^(2) =CD^2 +3BD^(2)` .

In the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE^(2)=3AC^(2)+5AD^(2).

In a right triangle ABC, right angled at B, if tan A=1, then verify that 2sinAcosA=1.

In the given fig. if AD bot BC Prove that AB^(2) + CD^(2) = BD^(2) + AC^(2) .

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

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).

ABC is right - angled triangle at B. Let D and E be any two point on AB and BC respectively . Prove that AE^2 + CD^2 = AC^2 + DE^2

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

ABC is a right angled isosceles triangles with angle B = 90 ^@ if D is a point on A B so that angle DCB = 15 ^@ and if Ad = 35 cm , then CD=

A(-3,2),B(3,2) and C(-3,-2) are the vertices of the right trinagle ,right angled at A. Show that the mid point of the hypotenus is equidistant form the vertices.