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).`

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) .

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 a right angled triangle in which /_A = 90^@ and AB = AC . Show that /_B = /_C .

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

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

The points A(-5,4), B(-1,-2) and C(5,2) are the vertices of an isosceles right angled trinagle where the right angle is at B. Find the corrdinates of D so that ABCD is a square .

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL^(2)+ CM^(2))=5BC^(2)

In a right angle triangle ABC, right angle is at C, BC+CA = 23 cm and BC-CA = 7cm ,then find sin A tan B

Solve the following sub question : In an equilateral triangle ABC, the side BC is trisected at D. prove that 9 AD^(2) = 7 AB^(2)